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
Correct Answer= A