Question

Find the areas of the figures for parts (a) and (b) below.

Answer 1

Case: Area of plane shapes

Method:

a) Parallelogram

To find the area we need to find the perpendicular height (using Pythagoras theorem)

`\begin{gathered} h^2+7^2=25^2 \\ h^2+49=625 \\ h^2=625-49 \\ h^2=576 \\ h=√(576) \\ h=24 \end{gathered}`

The Area of a parallelogram is given as:

`\begin{gathered} A=bh \\ A=23*24 \\ A=552\text{ }ft^2 \end{gathered}`

b) Triangle

To find the area of the triangle, we need to find the base first

First, lets find 'a'

`\begin{gathered} a^2+60^2=70^2 \\ a^2+3600=4900 \\ a^2=4900-3600 \\ a^=√(1300) \\ a=36.06 \end{gathered}`

The base, b

b= 2(a)

b= 2 (36.06)

b= 72.12

The area of the triangle is:

`\begin{gathered} A=(1)/(2)bh \\ A=(1)/(2)*72.12*60 \\ A=2163.6 \end{gathered}`

Final answer:

a) Parallelogram,

A= 552 square feet

b) Triangle

A= 2163.6 square feet