Math / Geometry

QuestionWhich figure has a greater area?

Studdy Solution

STEP 1

1. Both figures are right triangles.
2. The area of a right triangle can be calculated using the formula: $\frac{1}{2} \times \text{base} \times \text{height}$ .

STEP 2

1. Calculate the area of the left triangle.
2. Calculate the area of the right triangle.
3. Compare the areas to determine which is greater.

STEP 3

Calculate the area of the left triangle using the formula for the area of a right triangle:
$\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}$
Substitute the given values for the left triangle:
$\text{Area} = \frac{1}{2} \times 56 \text{ ft} \times 72 \text{ ft}$
Calculate the area:
$\text{Area} = \frac{1}{2} \times 4032 \text{ ft}^2$ $\text{Area} = 2016 \text{ ft}^2$

STEP 4

Calculate the area of the right triangle using the same formula:
$\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}$
Substitute the given values for the right triangle:
$\text{Area} = \frac{1}{2} \times 80 \text{ ft} \times 48 \text{ ft}$
Calculate the area:
$\text{Area} = \frac{1}{2} \times 3840 \text{ ft}^2$ $\text{Area} = 1920 \text{ ft}^2$

STEP 5

Compare the areas of the two triangles:
- Left triangle area: $2016 \text{ ft}^2$ - Right triangle area: $1920 \text{ ft}^2$
Since $2016 \text{ ft}^2 > 1920 \text{ ft}^2$ , the left triangle has a greater area.
The left triangle has the greater area.

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