Question

what is the area of the composite figure? units²

Explanation:

Step1: Divide the figure into simpler shapes

The figure can be divided into a rectangle and a trapezoid.

Step2: Calculate the area of the rectangle

The rectangle has length 6 and width 5. The area formula for a rectangle is $A = lw$. So, $A_{rectangle}=6\times5 = 30$.

Step3: Calculate the area of the trapezoid

The trapezoid has bases $b_1 = 6$ and $b_2=10$, and height $h=(5 + 2- 3)=4$. The area formula for a trapezoid is $A=\frac{(b_1 + b_2)h}{2}$. So, $A_{trapezoid}=\frac{(6 + 10)\times4}{2}=\frac{16\times4}{2}=32$.

Step4: Calculate the total area

The total area of the composite figure is the sum of the areas of the rectangle and the trapezoid. $A = A_{rectangle}+A_{trapezoid}=30 + 32=62$.

Answer:

62