Question

what is the area of this figure?
2 in
4 in
3 in
6 in
7 in
5 in
5 in
if necessary, round your answer to the nearest hundredth.
square inches

Explanation:

Step1: Identify the figure's components

The figure consists of a quarter-circle, a rectangle, and a smaller rectangle.

Step2: Calculate the quarter-circle area

Radius of the quarter-circle: $5 + 2 = 7$ in.
Area formula: $\frac{1}{4} \pi r^2$
$\frac{1}{4} \times 3.1416 \times 7^2 = \frac{1}{4} \times 3.1416 \times 49 ≈ 38.4846$ in².

Step3: Calculate the large rectangle area

Dimensions: $5$ in (width) × $7$ in (height).
Area: $5 \times 7 = 35$ in².

Step4: Calculate the small rectangle area

Dimensions: $3$ in (width) × $4$ in (height).
Area: $3 \times 4 = 12$ in².

Step5: Sum all areas

Total area: $38.4846 + 35 + 12 ≈ 85.48$ in².

Answer:

85.48