Question

find the area of the following shape. you must show all work to receive credit.

Explanation:

Step1: Divide the shape

Divide the shape into a triangle and a rectangle.

Step2: Calculate the area of the triangle

The formula for the area of a triangle is $A_{triangle}=\frac{1}{2}\times base\times height$. The base of the triangle is $4 - (- 4)=8$ units, and the height is $4 - 2 = 2$ units. So, $A_{triangle}=\frac{1}{2}\times8\times2=8$.

Step3: Calculate the area of the rectangle

The formula for the area of a rectangle is $A_{rectangle}=length\times width$. The length is $2$ units and the width is $2$ units. So, $A_{rectangle}=2\times2 = 4$.

Step4: Sum the areas

$A = A_{triangle}+A_{rectangle}=8 + 4$.

Answer:

$12$