Question

The side of a rhombus is 10 cm and one of its diagonals is 12 cm. Find its perimeter and area.​

Answer 1

The side of a rhombus is 10 cm and one of its diagonals is 12 cm. Find the perimeter and area


Perimeter = 10 * 4 = 40 cm
Measurement of the other diagonal
10^2 = d^2 + 6^2
d= 8
Other diagonal = 16 cm
So area = 1/2 * 16 *12 = 96 sq.cm

Answer 2

Answer:

Area = 96 cm²

Perimeter = 40 cm

Step-by-step explanation:

Area of a rhombus = 1/2 (diagonal 1 x diagonal 2)

Since we already know one of the diagonals, we need to find the other.

Find half the length of the other diagonal:

The two diagonals will bisect each other at right angle, so we can find half the length of the other diagonal using Pythagoras theorem.

a² + b² = c²

(12 ÷ 2)² + b² = 10²

6² + b² = 10²

b² = 10² - 6²

b² = 64

b = 8 cm

Find the length of the diagonal:

half the diagonal is 8 cm

Therefore the diagonal = 8 x 2 = 16 cm

Find the area of the rhombus:

Area = 1/2 ( 16 x 12)

Area = 96 cm²

Find the perimeter of the rhombus:

Perimeter = 4 x length

Perimeter = 4 x 10

Perimeter = 40 cm

Answer: 96 cm², 40 cm