Question

4.) heidi has a bag of mixed shapes. she chooses 3 shapes and fits them together to form a figure with the dimensions as shown.
8 m.
21 m.
what is the area of the figure heidi create use 3 for π.

Explanation:

Step1: Identify side lengths

The square has side $s=8$ m.
Length of the base segment for the triangle: $21 - 8 = 13$ m.
Radius of the quarter-circle: $r=8$ m.

Step2: Calculate area of square

Area formula: $A_{square}=s^2$
$A_{square}=8^2=64$ $\text{m}^2$

Step3: Calculate area of triangle

Area formula: $A_{triangle}=\frac{1}{2}bh$, where $b=13$ m, $h=8$ m
$A_{triangle}=\frac{1}{2} \times 13 \times 8=52$ $\text{m}^2$

Step4: Calculate area of quarter-circle

Area formula: $A_{quarter}=\frac{1}{4}\pi r^2$, use $\pi=3$
$A_{quarter}=\frac{1}{4} \times 3 \times 8^2=\frac{1}{4} \times 3 \times 64=48$ $\text{m}^2$

Step5: Sum all areas

Total area: $A_{total}=A_{square}+A_{triangle}+A_{quarter}$
$A_{total}=64+52+48$

Answer:

164 $\text{m}^2$