Question

use the given dimensions to calculate the total area of the figure. round your answer to the nearest tenth. 124.2 cm² 119.8 cm² 108.4 cm² 121.3 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 quarter - circle

The area formula for a full - circle is $A=\pi r^{2}$. For a quarter - circle with $r = 6$ in, $A_{quarter - circle}=\frac{1}{4}\pi r^{2}=\frac{1}{4}\pi\times6^{2}=\frac{1}{4}\pi\times36 = 9\pi\approx9\times3.14 = 28.26$ in².

Step4: Calculate total area

$A_{total}=A_{triangle}+A_{rectangle}+A_{quarter - circle}=7.5 + 50+28.26=85.76$ in².

Answer:

$85.76$ in²