Question

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

Explanation:

Step1: Divide the figure into a rectangle and a trapezoid

We can split the composite - figure into a rectangle with length 14 cm and width 5 cm and a trapezoid with bases \(b_1 = 5 + 2=7\) cm and \(b_2 = 5\) cm and height \(h = 14 - 5=9\) cm.

Step2: Calculate the area of the rectangle

The area formula for a rectangle is \(A_{rect}=l\times w\). Here, \(l = 14\) cm and \(w = 5\) cm, so \(A_{rect}=14\times5 = 70\) \(cm^{2}\).

Step3: Calculate the area of the trapezoid

The area formula for a trapezoid is \(A_{trap}=\frac{(b_1 + b_2)h}{2}\). Substitute \(b_1 = 7\) cm, \(b_2 = 5\) cm and \(h = 9\) cm into the formula: \(A_{trap}=\frac{(7 + 5)\times9}{2}=\frac{12\times9}{2}=54\) \(cm^{2}\).

Step4: Calculate the area of the composite figure

The area of the composite figure \(A = A_{rect}+A_{trap}\). \(A=70 + 35=105\) \(cm^{2}\).

Answer:

105 \(cm^{2}\)