Find the area of a rhombus with a perimeter equal to 40 and a diagonal equal to 14 cm.

about 100 cm²

Step-by-step explanation:

The side length of the rhombus is 1/4 of the perimeter so is 10 cm. The length of half of the other diagonal will be the length of the leg of a right triangle with hypotenuse 10 and leg 7 (half the given diagonal).

d = √ (10² - 7²) = √51

Then the area of the rhombus is the product of this and the given diagonal:

A = (14 cm) (√51 cm) ≈ 99.98 cm²

The area of the rhombus is about 100 cm².