what is the area of the composite figure? 70 cm² 100 cm² 105 cm² 130 cm²

Explanation:

Step1: Divide the figure into a trapezoid and a rectangle

The trapezoid has bases $b_1 = 5 + 5=10$ cm and $b_2 = 5$ cm, and height $h_1=14 - 2 = 12$ cm. The rectangle has length $l = 2$ cm and width $w = 5$ cm.

Step2: Calculate the area of the trapezoid

Use the trapezoid - area formula $A_1=\frac{(b_1 + b_2)h_1}{2}$. Substitute $b_1 = 10$ cm, $b_2 = 5$ cm, and $h_1 = 12$ cm. $A_1=\frac{(10 + 5)\times12}{2}=\frac{15\times12}{2}=90$ $cm^2$.

Step3: Calculate the area of the rectangle

Use the rectangle - area formula $A_2=l\times w$. Substitute $l = 2$ cm and $w = 5$ cm. $A_2=2\times5 = 10$ $cm^2$.

Step4: Calculate the area of the composite figure

$A=A_1 + A_2$. Substitute $A_1 = 90$ $cm^2$ and $A_2 = 10$ $cm^2$. $A=90+10 = 100$ $cm^2$.

Answer:

100 $cm^2$