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Math  /  Geometry

QuestionWhat is the area of this figure?

Studdy Solution

STEP 1

1. The figure is composed of a larger right triangle, a rectangle, and a smaller right triangle.
2. The dimensions provided are accurate and can be used to calculate the area of each shape.
3. The area of the composite figure is the sum of the areas of the individual shapes.

STEP 2

1. Calculate the area of the larger right triangle.
2. Calculate the area of the rectangle.
3. Calculate the area of the smaller right triangle.
4. Sum the areas of the individual shapes to find the total area of the composite figure.

STEP 3

Calculate the area of the larger right triangle using the formula for the area of a triangle:
Area=12×base×height \text{Area} = \frac{1}{2} \times \text{base} \times \text{height}
Substitute the given values:
Area=12×6 ft×6 ft \text{Area} = \frac{1}{2} \times 6 \text{ ft} \times 6 \text{ ft} =12×36 ft2 = \frac{1}{2} \times 36 \text{ ft}^2 =18 ft2 = 18 \text{ ft}^2

STEP 4

Calculate the area of the rectangle using the formula for the area of a rectangle:
Area=width×height \text{Area} = \text{width} \times \text{height}
Substitute the given values:
Area=4 ft×2 ft \text{Area} = 4 \text{ ft} \times 2 \text{ ft} =8 ft2 = 8 \text{ ft}^2

STEP 5

Calculate the area of the smaller right triangle using the formula for the area of a triangle:
Area=12×base×height \text{Area} = \frac{1}{2} \times \text{base} \times \text{height}
Substitute the given values:
Area=12×2 ft×2 ft \text{Area} = \frac{1}{2} \times 2 \text{ ft} \times 2 \text{ ft} =12×4 ft2 = \frac{1}{2} \times 4 \text{ ft}^2 =2 ft2 = 2 \text{ ft}^2

STEP 6

Sum the areas of the individual shapes to find the total area of the composite figure:
Total Area=18 ft2+8 ft2+2 ft2 \text{Total Area} = 18 \text{ ft}^2 + 8 \text{ ft}^2 + 2 \text{ ft}^2 =28 ft2 = 28 \text{ ft}^2
The area of the composite figure is:
28 ft2 \boxed{28 \text{ ft}^2}

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