A surveying problem uses Trapezoidal rule area (single panel). Given offset 1 (h1) = 32.0000 ft; offset 2 (h2) = 43.5000 ft; interval width (w) = 19.0000 ft, determine the area (A) in ft².

Start with the thinking

• The governing relation printed in this handbook section is Trapezoidal rule area (single panel).
• Everything except A is given, so isolate A symbolically first — never rearrange after the numbers are in.
• Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
• Surveying items reward recognising the unknown before touching a calculator.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$A = (h_1 + h_2)/2 \times w$$

2. Step 2 — Rearrange the relation so that A stands alone on the left-hand side.

3. Step 3

   $$List the givens: offset 1 (h_{1}) = 32.0000 ft, offset 2 (h_{2}) = 43.5000 ft, interval width (w) = 19.0000 ft$$

4. Step 4 — Substitute the given values into the rearranged relation.

5. Step 5 — Evaluate:

   $$A = 717.3\ \text{ft²}$$

6. Step 6 — Check: returning A = 717.3 ft² to

   $$A = (h_1 + h_2)/2 \times w$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• 1,435 — kept a factor of two that cancels in the correct rearrangement.
• 358.6 — dropped that same factor in the other direction.
• 789.0 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Surveying → Area formulas

A surveying problem uses Trapezoidal rule area (single panel). Given offset 1 (h1) = 42.0000 ft; offset 2 (h2) = 18.0000 ft; area (A) = 1,215 ft², determine the interval width (w) in ft.

Start with the thinking

• The governing relation printed in this handbook section is Trapezoidal rule area (single panel).
• Everything except w is given, so isolate w symbolically first — never rearrange after the numbers are in.
• Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
• Surveying items reward recognising the unknown before touching a calculator.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$A = (h_1 + h_2)/2 \times w$$

2. Step 2 — Rearrange the relation so that w stands alone on the left-hand side.

3. Step 3

   $$List the givens: offset 1 (h_{1}) = 42.0000 ft, offset 2 (h_{2}) = 18.0000 ft, area (A) = 1,215 ft^{2}$$

4. Step 4 — Substitute the given values into the rearranged relation.

5. Step 5 — Evaluate:

   $$w = 40.5000\ \text{ft}$$

6. Step 6 — Check: returning w = 40.5000 ft to

   $$A = (h_1 + h_2)/2 \times w$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• 81.0000 — kept a factor of two that cancels in the correct rearrangement.
• 20.2500 — dropped that same factor in the other direction.
• 44.5500 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Surveying → Area formulas

A surveying problem uses Trapezoidal rule area (single panel). Given offset 2 (h2) = 5.0000 ft; interval width (w) = 82.0000 ft; area (A) = 3,198 ft², determine the offset 1 (h1) in ft.

Start with the thinking

• The governing relation printed in this handbook section is Trapezoidal rule area (single panel).
• Everything except h1 is given, so isolate h1 symbolically first — never rearrange after the numbers are in.
• Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
• Surveying items reward recognising the unknown before touching a calculator.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$A = (h_1 + h_2)/2 \times w$$

2. Step 2 — Rearrange the relation so that h1 stands alone on the left-hand side.

3. Step 3

   $$List the givens: offset 2 (h_{2}) = 5.0000 ft, interval width (w) = 82.0000 ft, area (A) = 3,198 ft^{2}$$

4. Step 4 — Substitute the given values into the rearranged relation.

5. Step 5 — Evaluate:

   $$h_{1} = 73.0000\ \text{ft}$$

6. Step 6 — Check: returning h1 = 73.0000 ft to

   $$A = (h_1 + h_2)/2 \times w$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• 146.0 — kept a factor of two that cancels in the correct rearrangement.
• 36.5000 — dropped that same factor in the other direction.
• 80.3000 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Surveying → Area formulas

A surveying problem uses Trapezoidal rule area (single panel). Given offset 1 (h1) = 47.0000 ft; offset 2 (h2) = 19.0000 ft; interval width (w) = 15.0000 ft, determine the area (A) in ft².

Start with the thinking

• The governing relation printed in this handbook section is Trapezoidal rule area (single panel).
• Everything except A is given, so isolate A symbolically first — never rearrange after the numbers are in.
• Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
• Surveying items reward recognising the unknown before touching a calculator.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$A = (h_1 + h_2)/2 \times w$$

2. Step 2 — Rearrange the relation so that A stands alone on the left-hand side.

3. Step 3

   $$List the givens: offset 1 (h_{1}) = 47.0000 ft, offset 2 (h_{2}) = 19.0000 ft, interval width (w) = 15.0000 ft$$

4. Step 4 — Substitute the given values into the rearranged relation.

5. Step 5 — Evaluate:

   $$A = 495.0\ \text{ft²}$$

6. Step 6 — Check: returning A = 495.0 ft² to

   $$A = (h_1 + h_2)/2 \times w$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• 990.0 — kept a factor of two that cancels in the correct rearrangement.
• 247.5 — dropped that same factor in the other direction.
• 544.5 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Surveying → Area formulas

A surveying problem uses Trapezoidal rule area (single panel). Given offset 1 (h1) = 46.5000 ft; offset 2 (h2) = 44.5000 ft; area (A) = 1,078 ft², determine the interval width (w) in ft.

Start with the thinking

• The governing relation printed in this handbook section is Trapezoidal rule area (single panel).
• Everything except w is given, so isolate w symbolically first — never rearrange after the numbers are in.
• Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
• Surveying items reward recognising the unknown before touching a calculator.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$A = (h_1 + h_2)/2 \times w$$

2. Step 2 — Rearrange the relation so that w stands alone on the left-hand side.

3. Step 3

   $$List the givens: offset 1 (h_{1}) = 46.5000 ft, offset 2 (h_{2}) = 44.5000 ft, area (A) = 1,078 ft^{2}$$

4. Step 4 — Substitute the given values into the rearranged relation.

5. Step 5 — Evaluate:

   $$w = 23.6923\ \text{ft}$$

6. Step 6 — Check: returning w = 23.6923 ft to

   $$A = (h_1 + h_2)/2 \times w$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• 47.3846 — kept a factor of two that cancels in the correct rearrangement.
• 11.8462 — dropped that same factor in the other direction.
• 26.0615 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Surveying → Area formulas

A surveying problem uses Trapezoidal rule area (single panel). Given offset 2 (h2) = 9.0000 ft; interval width (w) = 37.0000 ft; area (A) = 2,645 ft², determine the offset 1 (h1) in ft.

Start with the thinking

• The governing relation printed in this handbook section is Trapezoidal rule area (single panel).
• Everything except h1 is given, so isolate h1 symbolically first — never rearrange after the numbers are in.
• Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
• Surveying items reward recognising the unknown before touching a calculator.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$A = (h_1 + h_2)/2 \times w$$

2. Step 2 — Rearrange the relation so that h1 stands alone on the left-hand side.

3. Step 3

   $$List the givens: offset 2 (h_{2}) = 9.0000 ft, interval width (w) = 37.0000 ft, area (A) = 2,645 ft^{2}$$

4. Step 4 — Substitute the given values into the rearranged relation.

5. Step 5 — Evaluate:

   $$h_{1} = 134.0\ \text{ft}$$

6. Step 6 — Check: returning h1 = 134.0 ft to

   $$A = (h_1 + h_2)/2 \times w$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• 267.9 — kept a factor of two that cancels in the correct rearrangement.
• 66.9865 — dropped that same factor in the other direction.
• 147.4 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Surveying → Area formulas

A surveying problem uses Trapezoidal rule area (single panel). Given offset 1 (h1) = 22.0000 ft; offset 2 (h2) = 19.5000 ft; interval width (w) = 22.0000 ft, determine the area (A) in ft².

Start with the thinking

• The governing relation printed in this handbook section is Trapezoidal rule area (single panel).
• Everything except A is given, so isolate A symbolically first — never rearrange after the numbers are in.
• Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
• Surveying items reward recognising the unknown before touching a calculator.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$A = (h_1 + h_2)/2 \times w$$

2. Step 2 — Rearrange the relation so that A stands alone on the left-hand side.

3. Step 3

   $$List the givens: offset 1 (h_{1}) = 22.0000 ft, offset 2 (h_{2}) = 19.5000 ft, interval width (w) = 22.0000 ft$$

4. Step 4 — Substitute the given values into the rearranged relation.

5. Step 5 — Evaluate:

   $$A = 456.5\ \text{ft²}$$

6. Step 6 — Check: returning A = 456.5 ft² to

   $$A = (h_1 + h_2)/2 \times w$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• 913.0 — kept a factor of two that cancels in the correct rearrangement.
• 228.3 — dropped that same factor in the other direction.
• 502.2 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Surveying → Area formulas

A surveying problem uses Trapezoidal rule area (single panel). Given offset 1 (h1) = 27.5000 ft; offset 2 (h2) = 43.0000 ft; area (A) = 1,168 ft², determine the interval width (w) in ft.

Start with the thinking

• The governing relation printed in this handbook section is Trapezoidal rule area (single panel).
• Everything except w is given, so isolate w symbolically first — never rearrange after the numbers are in.
• Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
• Surveying items reward recognising the unknown before touching a calculator.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$A = (h_1 + h_2)/2 \times w$$

2. Step 2 — Rearrange the relation so that w stands alone on the left-hand side.

3. Step 3

   $$List the givens: offset 1 (h_{1}) = 27.5000 ft, offset 2 (h_{2}) = 43.0000 ft, area (A) = 1,168 ft^{2}$$

4. Step 4 — Substitute the given values into the rearranged relation.

5. Step 5 — Evaluate:

   $$w = 33.1348\ \text{ft}$$

6. Step 6 — Check: returning w = 33.1348 ft to

   $$A = (h_1 + h_2)/2 \times w$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• 66.2695 — kept a factor of two that cancels in the correct rearrangement.
• 16.5674 — dropped that same factor in the other direction.
• 36.4482 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Surveying → Area formulas

A surveying problem uses Trapezoidal rule area (single panel). Given offset 2 (h2) = 42.0000 ft; interval width (w) = 53.0000 ft; area (A) = 2,777 ft², determine the offset 1 (h1) in ft.

Start with the thinking

• The governing relation printed in this handbook section is Trapezoidal rule area (single panel).
• Everything except h1 is given, so isolate h1 symbolically first — never rearrange after the numbers are in.
• Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
• Surveying items reward recognising the unknown before touching a calculator.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$A = (h_1 + h_2)/2 \times w$$

2. Step 2 — Rearrange the relation so that h1 stands alone on the left-hand side.

3. Step 3

   $$List the givens: offset 2 (h_{2}) = 42.0000 ft, interval width (w) = 53.0000 ft, area (A) = 2,777 ft^{2}$$

4. Step 4 — Substitute the given values into the rearranged relation.

5. Step 5 — Evaluate:

   $$h_{1} = 62.7925\ \text{ft}$$

6. Step 6 — Check: returning h1 = 62.7925 ft to

   $$A = (h_1 + h_2)/2 \times w$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• 125.6 — kept a factor of two that cancels in the correct rearrangement.
• 31.3962 — dropped that same factor in the other direction.
• 69.0717 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Surveying → Area formulas

A surveying problem uses Trapezoidal rule area (single panel). Given offset 1 (h1) = 26.0000 ft; offset 2 (h2) = 13.5000 ft; interval width (w) = 59.0000 ft, determine the area (A) in ft².

Start with the thinking

• The governing relation printed in this handbook section is Trapezoidal rule area (single panel).
• Everything except A is given, so isolate A symbolically first — never rearrange after the numbers are in.
• Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
• Surveying items reward recognising the unknown before touching a calculator.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$A = (h_1 + h_2)/2 \times w$$

2. Step 2 — Rearrange the relation so that A stands alone on the left-hand side.

3. Step 3

   $$List the givens: offset 1 (h_{1}) = 26.0000 ft, offset 2 (h_{2}) = 13.5000 ft, interval width (w) = 59.0000 ft$$

4. Step 4 — Substitute the given values into the rearranged relation.

5. Step 5 — Evaluate:

   $$A = 1165\ \text{ft²}$$

6. Step 6 — Check: returning A = 1,165 ft² to

   $$A = (h_1 + h_2)/2 \times w$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• 2,331 — kept a factor of two that cancels in the correct rearrangement.
• 582.6 — dropped that same factor in the other direction.
• 1,282 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Surveying → Area formulas