Question

find the area and the perimeter of a rhombus in which diagonals are 6cm and 8cm​

Answer 1

$\longrightarrow \: given \:$

✓ Diagonals of rhombus

Let the diagonals be d1 and d2.

d1 = 6 cm d2 = 8 cm

$\longrightarrow \: to \: find \:$

✓ Area and perimeter of rhombus

$\longrightarrow \: solution$

$area \: of \: rhombus \: = \frac{d1 \times d2}{2}$

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

$= 24 \: {cm}^{2}$

The diagonals of a rhombus bisect each other at 90° and all the sides of a rhombus are equal.

side of a rhombus should be found using Pythagoras theorem ,

Length of rhombus =

$\sqrt{ {6}^{2} } + {8}^{2} = \sqrt{36 + 64}$

$= \sqrt{100} = 10$

Now the side of rhombus is 10 cm

$perimeter \: of \: rhombus \: = 4 \times side$

$= 4 \times 10 = 40 \: cm$

Therefore

Area of rhombus = 24 sq.cm

Area of rhombus = 24 sq.cm Perimeter of rhombus = 40 cm

________________________