A surveyor computes the area of a parallelogram-shaped parcel. Given base (b) = 29.0000 ft; height (h) = 19.0000 ft, determine the area (A) in ft^2.

Start with the thinking

• The governing relation printed in this handbook section is Parallelogram area.
• 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.
• The parallelogram area formula relates the base and height of a parallelogram to its area.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$A = b \, h$$

2. Step 2 — Rearrange symbolically for A:

   $$A = b h$$

3. Step 3

   $$List the givens: base (b) = 29.0000 ft, height (h) = 19.0000 ft$$

4. Step 4 — Substitute the given values:

   $$A = 29.0000 19.0000$$

5. Step 5 — Evaluate:

   A = 551.0\ \text{ft^2}

6. Step 6 — Check: returning A = 551.0 ft^2 to

   $$A = b \, h$$

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

Why the other options are there

• 1,102 — kept a factor of two that cancels in the correct rearrangement.
• 275.5 — dropped that same factor in the other direction.
• 606.1 — rounded an intermediate value before the final step.

Reference: FE Handbook — Parallelogram

A drafter checks the area of a parallelogram panel. Given height (h) = 20.0000 ft; area (A) = 403.5 ft^2, determine the base (b) in ft.

Start with the thinking

• The governing relation printed in this handbook section is Parallelogram area.
• Everything except b is given, so isolate b 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.
• The parallelogram area formula relates the base and height of a parallelogram to its area.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$A = b \, h$$

2. Step 2 — Rearrange symbolically for b:

   $$b = \dfrac{A}{h}$$

3. Step 3

   $$List the givens: height (h) = 20.0000 ft, area (A) = 403.5 ft^2$$

4. Step 4 — Substitute the given values:

   $$b = \dfrac{403.5}{20.0000}$$

5. Step 5 — Evaluate:

   $$b = 20.1750\ \text{ft}$$

6. Step 6 — Check: returning b = 20.1750 ft to

   $$A = b \, h$$

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

Why the other options are there

• 40.3500 — kept a factor of two that cancels in the correct rearrangement.
• 10.0875 — dropped that same factor in the other direction.
• 22.1925 — rounded an intermediate value before the final step.

Reference: FE Handbook — Parallelogram

A student finds the height of a parallelogram given its area and base. Given base (b) = 4.0000 ft; area (A) = 320.5 ft^2, determine the height (h) in ft.

Start with the thinking

• The governing relation printed in this handbook section is Parallelogram area.
• Everything except h is given, so isolate h 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.
• The parallelogram area formula relates the base and height of a parallelogram to its area.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$A = b \, h$$

2. Step 2 — Rearrange symbolically for h:

   $$h = \dfrac{A}{b}$$

3. Step 3

   $$List the givens: base (b) = 4.0000 ft, area (A) = 320.5 ft^2$$

4. Step 4 — Substitute the given values:

   $$h = \dfrac{320.5}{4.0000}$$

5. Step 5 — Evaluate:

   $$h = 80.1250\ \text{ft}$$

6. Step 6 — Check: returning h = 80.1250 ft to

   $$A = b \, h$$

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

Why the other options are there

• 160.3 — kept a factor of two that cancels in the correct rearrangement.
• 40.0625 — dropped that same factor in the other direction.
• 88.1375 — rounded an intermediate value before the final step.

Reference: FE Handbook — Parallelogram

A surveyor computes the area of a parallelogram-shaped parcel. Given base (b) = 2.5000 ft; height (h) = 16.0000 ft, determine the area (A) in ft^2.

Start with the thinking

• The governing relation printed in this handbook section is Parallelogram area.
• 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.
• The parallelogram area formula relates the base and height of a parallelogram to its area.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$A = b \, h$$

2. Step 2 — Rearrange symbolically for A:

   $$A = b h$$

3. Step 3

   $$List the givens: base (b) = 2.5000 ft, height (h) = 16.0000 ft$$

4. Step 4 — Substitute the given values:

   $$A = 2.5000 16.0000$$

5. Step 5 — Evaluate:

   A = 40.0000\ \text{ft^2}

6. Step 6 — Check: returning A = 40.0000 ft^2 to

   $$A = b \, h$$

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

Why the other options are there

• 80.0000 — kept a factor of two that cancels in the correct rearrangement.
• 20.0000 — dropped that same factor in the other direction.
• 44.0000 — rounded an intermediate value before the final step.

Reference: FE Handbook — Parallelogram

A drafter checks the area of a parallelogram panel. Given height (h) = 16.0000 ft; area (A) = 88.0000 ft^2, determine the base (b) in ft.

Start with the thinking

• The governing relation printed in this handbook section is Parallelogram area.
• Everything except b is given, so isolate b 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.
• The parallelogram area formula relates the base and height of a parallelogram to its area.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$A = b \, h$$

2. Step 2 — Rearrange symbolically for b:

   $$b = \dfrac{A}{h}$$

3. Step 3

   $$List the givens: height (h) = 16.0000 ft, area (A) = 88.0000 ft^2$$

4. Step 4 — Substitute the given values:

   $$b = \dfrac{88.0000}{16.0000}$$

5. Step 5 — Evaluate:

   $$b = 5.5000\ \text{ft}$$

6. Step 6 — Check: returning b = 5.5000 ft to

   $$A = b \, h$$

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

Why the other options are there

• 11.0000 — kept a factor of two that cancels in the correct rearrangement.
• 2.7500 — dropped that same factor in the other direction.
• 6.0500 — rounded an intermediate value before the final step.

Reference: FE Handbook — Parallelogram

A student finds the height of a parallelogram given its area and base. Given base (b) = 6.5000 ft; area (A) = 199.0 ft^2, determine the height (h) in ft.

Start with the thinking

• The governing relation printed in this handbook section is Parallelogram area.
• Everything except h is given, so isolate h 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.
• The parallelogram area formula relates the base and height of a parallelogram to its area.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$A = b \, h$$

2. Step 2 — Rearrange symbolically for h:

   $$h = \dfrac{A}{b}$$

3. Step 3

   $$List the givens: base (b) = 6.5000 ft, area (A) = 199.0 ft^2$$

4. Step 4 — Substitute the given values:

   $$h = \dfrac{199.0}{6.5000}$$

5. Step 5 — Evaluate:

   $$h = 30.6154\ \text{ft}$$

6. Step 6 — Check: returning h = 30.6154 ft to

   $$A = b \, h$$

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

Why the other options are there

• 61.2308 — kept a factor of two that cancels in the correct rearrangement.
• 15.3077 — dropped that same factor in the other direction.
• 33.6769 — rounded an intermediate value before the final step.

Reference: FE Handbook — Parallelogram

A surveyor computes the area of a parallelogram-shaped parcel. Given base (b) = 26.5000 ft; height (h) = 7.5000 ft, determine the area (A) in ft^2.

Start with the thinking

• The governing relation printed in this handbook section is Parallelogram area.
• 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.
• The parallelogram area formula relates the base and height of a parallelogram to its area.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$A = b \, h$$

2. Step 2 — Rearrange symbolically for A:

   $$A = b h$$

3. Step 3

   $$List the givens: base (b) = 26.5000 ft, height (h) = 7.5000 ft$$

4. Step 4 — Substitute the given values:

   $$A = 26.5000 7.5000$$

5. Step 5 — Evaluate:

   A = 198.8\ \text{ft^2}

6. Step 6 — Check: returning A = 198.8 ft^2 to

   $$A = b \, h$$

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

Why the other options are there

• 397.5 — kept a factor of two that cancels in the correct rearrangement.
• 99.3750 — dropped that same factor in the other direction.
• 218.6 — rounded an intermediate value before the final step.

Reference: FE Handbook — Parallelogram

A drafter checks the area of a parallelogram panel. Given height (h) = 1.0000 ft; area (A) = 404.5 ft^2, determine the base (b) in ft.

Start with the thinking

• The governing relation printed in this handbook section is Parallelogram area.
• Everything except b is given, so isolate b 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.
• The parallelogram area formula relates the base and height of a parallelogram to its area.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$A = b \, h$$

2. Step 2 — Rearrange symbolically for b:

   $$b = \dfrac{A}{h}$$

3. Step 3

   $$List the givens: height (h) = 1.0000 ft, area (A) = 404.5 ft^2$$

4. Step 4 — Substitute the given values:

   $$b = \dfrac{404.5}{1.0000}$$

5. Step 5 — Evaluate:

   $$b = 404.5\ \text{ft}$$

6. Step 6 — Check: returning b = 404.5 ft to

   $$A = b \, h$$

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

Why the other options are there

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

Reference: FE Handbook — Parallelogram

A student finds the height of a parallelogram given its area and base. Given base (b) = 6.0000 ft; area (A) = 461.0 ft^2, determine the height (h) in ft.

Start with the thinking

• The governing relation printed in this handbook section is Parallelogram area.
• Everything except h is given, so isolate h 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.
• The parallelogram area formula relates the base and height of a parallelogram to its area.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$A = b \, h$$

2. Step 2 — Rearrange symbolically for h:

   $$h = \dfrac{A}{b}$$

3. Step 3

   $$List the givens: base (b) = 6.0000 ft, area (A) = 461.0 ft^2$$

4. Step 4 — Substitute the given values:

   $$h = \dfrac{461.0}{6.0000}$$

5. Step 5 — Evaluate:

   $$h = 76.8333\ \text{ft}$$

6. Step 6 — Check: returning h = 76.8333 ft to

   $$A = b \, h$$

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

Why the other options are there

• 153.7 — kept a factor of two that cancels in the correct rearrangement.
• 38.4167 — dropped that same factor in the other direction.
• 84.5167 — rounded an intermediate value before the final step.

Reference: FE Handbook — Parallelogram

A surveyor computes the area of a parallelogram-shaped parcel. Given base (b) = 14.0000 ft; height (h) = 1.5000 ft, determine the area (A) in ft^2.

Start with the thinking

• The governing relation printed in this handbook section is Parallelogram area.
• 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.
• The parallelogram area formula relates the base and height of a parallelogram to its area.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$A = b \, h$$

2. Step 2 — Rearrange symbolically for A:

   $$A = b h$$

3. Step 3

   $$List the givens: base (b) = 14.0000 ft, height (h) = 1.5000 ft$$

4. Step 4 — Substitute the given values:

   $$A = 14.0000 1.5000$$

5. Step 5 — Evaluate:

   A = 21.0000\ \text{ft^2}

6. Step 6 — Check: returning A = 21.0000 ft^2 to

   $$A = b \, h$$

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

Why the other options are there

• 42.0000 — kept a factor of two that cancels in the correct rearrangement.
• 10.5000 — dropped that same factor in the other direction.
• 23.1000 — rounded an intermediate value before the final step.

Reference: FE Handbook — Parallelogram