Question

Find the area of the irregular polygon to the right show all work

Answer 1

We are given an irregular pentagon. To calculate the area, we will have to break the pentagon into component shapes

We can break the pentagon into a trapezium and a triangle

The dimensions of the trapezium are :

1st base = 3 units

2nd base = 4 units

Height = 3 units

`\begin{gathered} Area\text{ of the trapezium = }(1)/(2)(a+b)h \\ =(1)/(2)(3+4)(3) \\ =10.5\text{ square unit} \end{gathered}`

The dimensions of the triangle are:

Base= 4 units

Height=2 units

`\begin{gathered} Area\text{ of the triangle = }(1)/(2)\text{ x base x height} \\ =(1)/(2)\text{ x 4 x 2} \\ =4\text{ square units} \end{gathered}`

Area of the polygon = area of trapezium + area of triangle

= 10.5 square unit + 4 square unit = 14.5 square unit

The answer is 14.5 square units