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 created?
use 3 for π.

Explanation:

Step1: Identify the 3 shapes

The figure is composed of a quarter-circle, a square, and a right triangle.

Step2: Find square side length

The top side of the square is 8 m, so its side length $s=8$ m.
Area of square: $A_{square}=s^2=8^2=64$ m²

Step3: Calculate quarter-circle area

Radius of the quarter-circle $r=8$ m, use $\pi=3$.
Area of quarter-circle: $A_{circle}=\frac{1}{4}\pi r^2=\frac{1}{4}\times3\times8^2=\frac{1}{4}\times3\times64=48$ m²

Step4: Find triangle base length

Total bottom length is 21 m, subtract square side: $b=21-8=13$ m.
Triangle height $h=8$ m.
Area of triangle: $A_{triangle}=\frac{1}{2}\times b\times h=\frac{1}{2}\times13\times8=52$ m²

Step5: Sum all areas

Total area: $A_{total}=A_{square}+A_{circle}+A_{triangle}$

Answer:

$64 + 48 + 52 = 164$ m²