Two squares are attached to the sides of a quarter circle as shown.
what is the best approximation for the area of this figure?
use 3.14 to approximate pi.
178.5 mm²
215.7 mm²
231.8 mm²
278.5 mm²

The answer is 278 mm²

The figure actually consists of 2 squares which side is 10 mm and a quarter circle with radius of 10 mm. Thus, the total area fo the figure (A) is the sum of 2 areas of the square (A1) and one-quarter of the area of a circle (A2):
A = 2A1 + 1/4A2

The area of the square (A1) with side s is:
A1 = s²
s = 10 mm
A1 = (10 mm)² = 100 mm²

The area of the circle (A2) with radius r is:
A2 = r² π
r = 10 mm
π = 3.15
A2 = (10 mm)² * 3.14 = 314 mm²

The total area is:
A = 2A1 + 1/4A2
A1 = 100 mm²
A2 = 314 mm²

A = 2 * 100 mm² + 1/4 * 314 mm²
A = 200 mm² + 78.5 mm²
A = 278 mm²