# What is the ratio of Area (AGH) to CD for Rhombus ABCD

Rhombus ABCD below is divided into three areas with AGH = 1/3rd Area of ABCD, ECF = 1/5th Area of ABCD. What is the ratio of Area (AGH) to CD, given that AC=12 and BD =16?

a) 10/3
b) 11/3
c) 13/3
d) 17/3
e) 19/3

Solution

To solve this question, you have to know the formula to find the area of a Rhombus.

The most common formulas and properties to remember in a Rhombus are

1) Area = base x altitude

2) Altitude
=
½ x sqrt (diagonal1^2 + diagonal2^2)

3) Area = (
diagonal1 X diagonal2)/2

4) All the sides are equal in a Rhombus

Next Steps

Draw an altitude AJ

Area of Rhombus ABCD = AJ x AB

AGH = 1/3rd Area of ABCD, ECF = 1/5th Area of ABCD.

Let each side of the Rhombus be equal to “a”

Altitude = ½ x sqrt (diagonal1^2 + diagonal2^2)

AJ = ½ x sqrt(ac^2 + bd^2)

AJ = 20/2 = 10

Area AGH = 1/3 (Area of ABCD) = 1/3 (AJ x AB)

Since all the sides in a Rhombus are equal

AB = BC = CD = DA = a

Area AGH = 1/3 (AJ x a)

(Area AGH)/CD =1/3 x (AJ x a)/a

= AJ

= 10/3

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