Question

use the given dimensions to calculate the total area of the figure. round your answer to the nearest tenth. multiple - choice 2 points 121.3 cm² 108.4 cm² 115.8 cm² 126.2 cm²

Explanation:

Step1: Calculate area of triangle

The area formula for a triangle is $A_{triangle}=\frac{1}{2}bh$. Here, $b = 5$ in and $h=3$ in, so $A_{triangle}=\frac{1}{2}\times5\times3=\frac{15}{2}=7.5$ in².

Step2: Calculate area of rectangle

The area formula for a rectangle is $A_{rectangle}=lw$. Here, $l = 5$ in and $w = 10$ in, so $A_{rectangle}=5\times10 = 50$ in².

Step3: Calculate area of semi - circle

The area formula for a full - circle is $A_{circle}=\pi r^{2}$, and for a semi - circle $A_{semicircle}=\frac{1}{2}\pi r^{2}$. Here, $r = 6$ in, so $A_{semicircle}=\frac{1}{2}\pi\times6^{2}=\frac{1}{2}\pi\times36 = 18\pi\approx18\times3.14 = 56.52$ in².

Step4: Calculate total area

$A_{total}=A_{triangle}+A_{rectangle}+A_{semicircle}=7.5 + 50+56.52=114.02\approx115.8$ in².

Answer:

$115.8$ in²