Question

the figure below is made of a triangle and half - circles. area of triangle = 448 square in. area of half circles = square in. 1024π 384π 128π

Explanation:

Step1: Identify radius of half - circles

The diameter of each half - circle is 32 in, so the radius $r=\frac{32}{2}=16$ in.

Step2: Calculate area of one half - circle

The area formula for a full - circle is $A = \pi r^{2}$. The area of a half - circle is $A_{half}=\frac{1}{2}\pi r^{2}$. Substituting $r = 16$ in, we get $A_{half}=\frac{1}{2}\pi(16)^{2}=\frac{1}{2}\pi\times256 = 128\pi$ square in.

Step3: Calculate area of three half - circles

Since there are 3 half - circles, the total area of the half - circles is $A_{total}=3\times128\pi=384\pi$ square in.

Answer:

384 $\pi$ square in