Question

What is the area of this polygon?

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units²
5-sided polygon on a coordinate plane with vertices g, p, e, s, t. point g is at (negative 3, 4), p is at (2, 4), e is at (4, 2), s is at (2, negative 3), t is at (negative 3, negative 3).

Answer 1

42 sq units

Explanation:

A diagram is attached.

These points form a pentagon. This pentagon can be split into a rectangle and a triangle.

The dimensions of the rectangle in the diagram are 5 by 7; this makes an area of A = 5(7) = 35 sq. un.

The dimensions of the triangle in the diagram are a base of 7 and a height of 2. This makes the area

A = 1/2bh = 1/2(7)(2) = 1/2(14) = 7 sq. un.

This makes the total area

35+7 = 42 sq. units.

Answer 2

42 sq. un.

Explanation:

Consider pentagon GPEST. The area of this pentegon consists of the sum of the area of the rectangle GPST and the area of the triangle PES.

1. The rectangle GPST has sides lengths of 5 un. and 7 un.. Thus, the area of the rectangle GPST is

`A_(GPST)=7\cdot 5=35\ un^2.`

2. The area of the triangle PES can be calculated as

`A_(PES)=(1)/(2)\cdot PS\cdot h,`

where h is the height drawn to the side PS. Since PS=7 un., then

`A_(PES)=(1)/(2)\cdot 7\cdot 2=7\ un^2.`

Therefore,

`A_(GPEST)=A_(GPST)+A_(PES)=35+7=42\ un^2.`