Question

determine the area of the composite figure. the curve is a semi - circle. a) about 13.7 cm² b) about 7.4 cm² c) about 6.3 cm² d) about 10.0 cm²

Explanation:

Step1: Calculate area of triangle

The area formula for a right - triangle is $A_{triangle}=\frac{1}{2}bh$. Here, $b = 3.7$ cm and $h=2.0$ cm. So $A_{triangle}=\frac{1}{2}\times3.7\times2.0 = 3.7$ $cm^2$.

Step2: Calculate area of semi - circle

The area formula for a circle is $A=\pi r^{2}$, and for a semi - circle $A_{semicircle}=\frac{1}{2}\pi r^{2}$. Given $r = 2.0$ cm, then $A_{semicircle}=\frac{1}{2}\times\pi\times(2.0)^{2}=\frac{1}{2}\times\pi\times4.0\approx\frac{1}{2}\times3.14\times4.0 = 6.28$ $cm^2$.

Step3: Calculate area of composite figure

The area of the composite figure $A = A_{triangle}+A_{semicircle}=3.7 + 6.28=9.98\approx10.0$ $cm^2$.

Answer:

d. About 10.0 $cm^2$