Answer to Question #163738 in Geometry for AYRIAH

Question

The base of the prism is a rhombus of side 20 cm with one diagonal 24 cm. Find the area of the base.

Answer 1

Area of a rhombus = (P*Q)/2

Where P are Q are the two diagonals of the rhombus.

One diagonal let us say P is given as 24cm.

Using 24 cm and one side of the given sides (20 cm), we will apply pythagoras theorem to calculate the missing diagonal, Q.

Now Q = 2* square root of (20² - 12²)

Q = 2* square root of (400 - 144)

Q = 2* square root of (256)

Q = 2* 16

Q = 32

Area of a rhombus = (P*Q)/2

Therefore;

Area = (32*24)/2

Area = 384 cm²