Question

1. determine the area of the composite figure. 13.5 mm 20 mm 9.5 mm

Explanation:

Step1: Calculate the area of the rectangle

The formula for the area of a rectangle is \(A = l\times w\). Here, \(l = 13.5\) mm and \(w=9.5\) mm.
\(A_{rectangle}=13.5\times9.5 = 128.25\) \(mm^{2}\)

Step2: Calculate the area of the trapezoid

The formula for the area of a trapezoid is \(A=\frac{(a + b)h}{2}\). But we can also think of the composite - figure as a combination of a rectangle and a triangle (by splitting the non - rectangular part). The base of the triangle is \(20 - 13.5=6.5\) mm and the height of the triangle is \(9.5\) mm. The formula for the area of a triangle is \(A=\frac{1}{2}\times base\times height\).
\(A_{triangle}=\frac{1}{2}\times6.5\times9.5=\frac{61.75}{2}=30.875\) \(mm^{2}\)

Step3: Calculate the total area of the composite figure

The total area \(A = A_{rectangle}+A_{triangle}\)
\(A=128.25 + 30.875=159.125\) \(mm^{2}\)

Answer:

\(159.125\) \(mm^{2}\)