Question

What is the length of a diagonal and area of a rhombus, if the length of its side is 10 cm, and the length of the other diagonal is 12 cm?

Answer 1

The area of rhombus is 96 cm² and the length of other diagonal is 16 cm.

Explanation:

Refer the figure given.

Using Pythagoras theorem to get half length of unknown diagonal

l =
`√(10^2-6^2) =8cm`

Length of unknown diagonal = 2l = 2 x 8 = 16 cm

Area of rhombus is half of product of diagonals.

`\texttt{Area = }(1)/(2)* 12* 16=96cm^2`

Answer 2

The side of a rhombus and the half-diagonals form a right triangle. The length of the other half-diagonal is found from the Pythagorean theorem to be

... d = √((10 cm)² -(6 cm)²) = √(64 cm²) = 8 cm

The length of the other diagonal is 16 cm.

The area is half the product of the diagonal lengths, so is

... area = (1/2)(12 cm)(16 cm) = 96 cm²