Question

The perimeter of a rhombus is 40. What is the area of the square?

Answer 1

Answer:96 cm squared

Explanation:

A rhombus has 4 edges of equal length. If it has perimeter of 40cm, then each length would be

40cm

4 = 10cm

Divide the rhombus into 4 right-angle triangle by cutting along the 2 diagonals.

Each right-angle triangle will have a hypotenuse of 10cm and one other edge with length

12cm

2 = 6cm

Use Pythagoras Theorem to find the length of the remaining edge.

√(10cm) squared − (6cm) squared = 8cm

Now find the area of the triangle.

1

2 × 6cm ×8cm =24cm squared

Since the original rhombus was made up of four such triangles, the area of the rhombus would be

24cm squared × 4 = 96cm squared

Explanation:

Answer 2

96 cm squared

Explanation:

A rhombus has 4 edges of equal length. If it has perimeter of 40cm, then each length would be

40cm

4 = 10cm

Divide the rhombus into 4 right-angle triangle by cutting along the 2 diagonals.

Each right-angle triangle will have a hypotenuse of 10cm and one other edge with length

12cm

2 = 6cm

Use Pythagoras Theorem to find the length of the remaining edge.

√(10cm) squared − (6cm) squared = 8cm

Now find the area of the triangle.

1

2 × 6cm ×8cm =24cm squared

Since the original rhombus was made up of four such triangles, the area of the rhombus would be

24cm squared × 4 = 96cm squared