Question

The diagonals of this rhombus are 8 and 16 units long. Their intersection creates four right angles, two 4-unit-long segments, and two 8-unit long segments. Given this information, find the area of the rhombus in square units (Use only the digits 0 – 9 and the decimal point, if needed, to enter a number).

Answer 1

`64\ \text{sq. units}`

Explanation:

Area of a rhombus is the product of the length of the diagonals divided by two.

Length of one diagonal is 8 units and the other diagonal is 16 units

Area is given by

`A=(8* 16)/(2)\\\Rightarrow A=64\ \text{sq. units}`

The area of the rhombus is
`64\ \text{sq. units}`

Another approach is the diagonals have created 4 triangles where the base and is height is either 4 units long or 8 units long so the area of the rhombus would be the area of the 4 triangles.

`A=4* (1)/(2)* 4* 8\\\Rightarrow A=64\ \text{sq. units}`