Question

part 1 of 2
find the area of the figure.
use the following formula
total area = area of a parallelogram + area of trapezoid
= 12·□+\frac{1}{2}·□·□·9
=□·54
=□²
(type integers or fractions.)

Explanation:

Step1: Identify shapes and formulas

The figure is composed of a parallelogram and a trapezoid. Area of parallelogram \(A_{1}=b\times h\), area of trapezoid \(A_{2}=\frac{1}{2}(a + b)h\).

Step2: Calculate area of parallelogram

For the parallelogram, base \(b = 12m\) and height \(h=4m\). So \(A_{1}=12\times4 = 48m^{2}\).

Step3: Calculate area of trapezoid

For the trapezoid, the parallel - sides are \(a = 12m\) and \(b = 8m\), and height \(h=(9 - 4)=5m\). Then \(A_{2}=\frac{1}{2}(12 + 8)\times5=\frac{1}{2}\times20\times5=50m^{2}\).

Step4: Calculate total area

Total area \(A=A_{1}+A_{2}=48 + 50=98m^{2}\).

Answer:

\(98m^{2}\)