Given a sided polygon with triangular hole
To Determine: The area of the shape
Solution:
The area of the shape is the area of the rectangle minus the area of the triangle
The formula for finding the area of a rectangle is
[tex]\begin{gathered} A_{\text{rectangle}}=\text{length}\times width \\ Given\colon\text{length}=15\operatorname{cm} \\ \text{width}=8\operatorname{cm} \\ A_{\text{rectangle}}=15\operatorname{cm}\times8\operatorname{cm}=120\operatorname{cm}^2 \end{gathered}[/tex]
The formula for finding the area of a triangle is
[tex]\begin{gathered} A_{\text{triangle}}=\frac{1}{2}\times base\times height \\ \text{Given:} \\ \text{base}=8\operatorname{cm} \\ \text{height}=4\operatorname{cm} \\ A_{\text{triangle}}=\frac{1}{2}\times8\operatorname{cm}\times4\operatorname{cm} \\ A_{\text{triangle}}=16\operatorname{cm}^2 \end{gathered}[/tex]
Therefore:
[tex]\begin{gathered} A_{\text{shape}}=A_{\text{rectangle}}-A_{\text{triangle}} \\ A_{shape}=120\operatorname{cm}-16\operatorname{cm}^2 \\ A_{\text{shape}}=104\operatorname{cm}^2 \end{gathered}[/tex]
Hence, the area of the given figure is 104cm²
