Q. 8 - Geometry

Question

Find the area of each figure:

Step-by-Step Solution

Answer

The area of given figure is44 square units.

Step 1. Given information.

It can be seen that the lower part of the figure is a rectangle with length 8 and 4 width

The upper part of the figure is an isosceles triangle with sides $5,5,8$

Step 2. Find the area of lower part.

Since the lower part is a rectangle and area of rectangle can be found using the formula $A=lb$

Where,

i= Length of a rectangle andb=  Width of a rectangle

So, the area of lower part$A_1=8\times 4$

                                            =32

Step 3. Find the area of upper part.

As the upper part of the figure is an isosceles triangle and the area of an triangle can be found using

$A=\frac{1}{2}bh$

b= Base of a triangle and h= Height of a triangle

Step 4. Find the Height of triangle.

We use Pythagorean Theorem. 

Pythagorean Theorem define that in a right angle triangle, the square of the hypotenuse is equal to the sum of squares of other sides.

$5^2=P^2+4^2$

$P^2=25-16$

$P^2=9$

$P=3$

Thus, the area of triangle

$A_2=\frac{1}{2}\left(3\right)\left(8\right)$

   $=12$  

Step 5. Find the total area.

 Total area of the figure $A=A_1+A_2$

                                             $=32+12$         

                                                =44     Square units

Therefore, the area of given figure is44 square units.