Question

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

Explanation:

Step1: Divide the figure into shapes

Divide the composite - figure into a rectangle and a trapezoid. The rectangle has dimensions \(2\times5\) and the trapezoid has bases \(5 + 5=10\) cm and \(5\) cm and height \(14 - 2=12\) cm.

Step2: Calculate the area of the rectangle

The area formula for a rectangle is \(A_{rect}=l\times w\). Here, \(l = 2\) cm and \(w = 5\) cm, so \(A_{rect}=2\times5=10\) \(cm^{2}\).

Step3: Calculate the area of the trapezoid

The area formula for a trapezoid is \(A_{trap}=\frac{(b_1 + b_2)h}{2}\), where \(b_1 = 10\) cm, \(b_2 = 5\) cm and \(h = 12\) cm. So \(A_{trap}=\frac{(10 + 5)\times12}{2}=\frac{15\times12}{2}=90\) \(cm^{2}\).

Step4: Calculate the total area

The total area of the composite - figure \(A = A_{rect}+A_{trap}\). So \(A=10 + 90=100\) \(cm^{2}\).

Answer:

100 \(cm^{2}\)