Question

find the area of the following figure with the indicated dimensions. use $pi = 3.14$. round your answer to the nearest hundredth, if necessary. answer how to enter your answer (opens in new window)

Explanation:

Step1: Find radius of semi - circle

The diameter of the semi - circle is 20.6 cm. The radius $r=\frac{20.6}{2}=10.3$ cm.

Step2: Calculate area of semi - circle

The area of a full - circle is $A_{circle}=\pi r^{2}$. The area of a semi - circle $A_{semicircle}=\frac{1}{2}\pi r^{2}$. Substituting $r = 10.3$ cm and $\pi=3.14$, we get $A_{semicircle}=\frac{1}{2}\times3.14\times(10.3)^{2}=\frac{1}{2}\times3.14\times106.09 = 166.6123$ $cm^{2}$.

Step3: Calculate area of triangle

The base of the triangle is 20.6 cm and the height is 25 cm. The area of a triangle $A_{triangle}=\frac{1}{2}\times base\times height=\frac{1}{2}\times20.6\times25=257.5$ $cm^{2}$.

Step4: Calculate total area of the figure

The total area $A = A_{semicircle}+A_{triangle}=166.6123 + 257.5=424.1123\approx424.11$ $cm^{2}$.

Answer:

424.11 $cm^{2}$