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ABCD is a trapezium with ab parallel to CD and the diagonals intersect at a point P the area of triangle ABP is 32 CM square and the area of triangle sea DP is 50 cm square the area of trapezium is

ABCD is a trapezium with ab parallel to CD and the diagonals intersect at a point P the area of triangle ABP is 32 CM square and the area of triangle sea DP is 50 cm square the area of trapezium is

Grade:8

1 Answers

Arun
25750 Points
4 years ago
The area of Trapezium = 1/2(AB+CD).H 
Let AB = 4x & CD = 5x (since you already found that sides are in 4:5) 
Let the heights be h1 & h2 respectively. 
Then H = h1 + h2 
Area = 1/2 * (4x+5x)(h1+h2) 
= 1/2 * 9x * h1 + 1/2 * 9x * h2 
1/2 * 4x*h1 = 32 
1/2 * 9x*h1 = 32 * 9/4 = 72 
1/2 * 5x * h2 = 50 
1/2 * 9x * h2 = 50 * 9/5 = 90 
Area = 72 + 90 = 162
 

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