Question

Can someone pls help me?!

Given a rhombus with side length of 10cm and one diagonal that is 12cm, find the length of the other diagonal and the area of this rhombus

Answer 1

A rhombus is parallel, so it would be 2 sides that are 10cm and the other 2 would be 12 cm. 10 x 12 = 120 cm is the area

Answer 2

• 16 cm
• 96 cm²

Explanation:

The diagonals of a rhombus are perpendicular to and bisect each other.

The diagonals divide the rhombus into four equal right triangles, with legs equal to half-diagonals and each side of a rhombus is a hypotenuse of the formed triangles.

Let the diagonals be x and y and sides be s.

According to Pythagorean we have:

• (x/2)² + (y/2)² = s²

Given:

• s = 10
• x = 12

Find y:

• (12/2)² + (y/2)² = 10²
• y²/4 = 100 - 36
• y² = 64*4
• y = 16 cm

Area of the rhombus:

• A = xy/2
• A = 12*16/2 = 96 cm²