Question

Find the area of the pentagon in the diagram below. A 15 square inches B 20 square inches C25 square inches D 28 square inches

Answer 1

we divide the pentagon into two figures

Trapezium

trapezium area

`\begin{gathered} A=((B+b)* h)/(2) \\ \\ A=((6+2)*4)/(2) \\ \\ A=16 \end{gathered}`

the are of the trapezium is 16 square in

Triangle

triangle area

`\begin{gathered} A=(b* h)/(2) \\ \\ A=(6*3)/(2) \\ \\ A=9 \end{gathered}`

the area of the triangle is 9 square in

Total area

Sum the areas to find the area of the pentagon

`\begin{gathered} 16+9 \\ =25 \end{gathered}`

the pentagon area is 25 square inches