Question

Find the area of the composite figure.19 mm 25 mm 3 mm 6mm

Answer 1

The figure consists of a rectangle and 2 right triangles, as shown in the diagram below

The areas of a rectangle and a triangle are given by the following formulas

$\begin{gathered} A_{\text{rectangle}}=lw \\ A_{\text{triangle}}=\frac{1}{2}b\cdot h \end{gathered}$

In our case,

$\begin{gathered} A_{\text{rectangle}}=6\cdot19=114 \\ A_{\text{triangle}}=\frac{1}{2}(25-19)\cdot(3+3)=\frac{1}{2}\cdot6\cdot6=\frac{36}{2}=18 \end{gathered}$

Thus,

$\begin{gathered} A_{\text{figure}}=A_{\text{rectangle}}+2A_{\text{triangle}}=114+36=150 \\ \Rightarrow A_{\text{figure}}=150 \end{gathered}$

The total area is 150mm^2