What is the area of rhombus abcd ?

The area is 36 units squared.

You have three ways you can solve this question.

Method 1:

Split the rhombus into two equal triangles.
You will get triangle ACD and triangle ACB.

Count the base length and height length of each triangle using the diagram.
You will get base = 6 units and height = 6 units. Plug this into the area of a triangle and then multiply it by 2.

A = bh/2 * 2
A = 6(6) / 2 * 2
A = 36 / 2 * 2
A = 18 * 2
A = 36

Method 2:

Calculate the length of DP.
The length of line segment DP is √28.8

Calculate the length of DC.
The length of line segment DC is 3√5

Put into equation A = bh.

A = bh
A = 3√5(√28.8)
A = 36

Method 3:

Calculate the length of each diagonal and put into formula A = 1/2(d1 * d2)

Diagonal DB = 12 units
Diagonal AC = 6 units

A = 1/2(d1 * d2)
A = 1/2(12 * 6)
A = 1/2(72)
A = 36

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