Q8.

Find the area of each figure:

Verified

Answer

The area of given figure is24 square units.

1Step 1. Given information.

Given figure is a rhombus.

The side of rhombus is 5 and one of its diagonal is 8.

2Step 2. Concept used.

Area of rhombus can be found using the diagonals

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

Where $d_{1} d_{2}$ , are the two diagonals of rhombus.

3Step 3. Find the diagonal of rhombus.

We can 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.

Using Pythagorean Theorem in $△ A O B$

$A B^{2} = O A^{2} + O B^{2}$

$5^{2} = 4^{2} + O B^{2}$

$25 = 16 + O B^{2}$

$O B^{2} = 9$

$O B = 3$

Thus, the another diagonal is $B D = O B + O D = 3 + 3 = 6$

4Step 4. Find the area of given figure.

Area of the rhombus

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

$= \frac{1}{2} \times 6 \times 8$

$= 24$ Square units.

Therefore, the area of given figure is 24square units.