In a parallelogram ABCD, point P lies in DC such that DP : PC = 3 : 2. If area of Δ DPB = 30 sq.cm, find the area of the parallelogram ABCD.
Theorems on Area
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Question

In a parallelogram ABCD, point P lies in DC such that DP : PC = 3 : 2. If area of Δ DPB = 30 sq.cm, find the area of the parallelogram ABCD.

KnowledgeBoat · Accepted Answer

Given, DP : PC = 3 : 2 We know that, Ratio of the area of triangles with same vertex and bases along the same line is equal to the ratio of their respective bases. From figure, Area of Δ CDB = Area of Δ PCB + Area of Δ DPB = 20 + 30 = 50 cm². Since, diagonal divides a || gm into two triangles of equal area. ∴ Area of || gm ABCD = 2 Area of Δ CDB = 2 × 50 = 100 cm². Hence, area of \\ gm ABCD = 100 cm².

Mathematics

In a parallelogram ABCD, point P lies in DC such that DP : PC = 3 : 2. If area of Δ DPB = 30 sq.cm, find the area of the parallelogram ABCD.

Theorems on Area

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Mathematics

In a parallelogram ABCD, point P lies in DC such that DP : PC = 3 : 2. If area of Δ DPB = 30 sq.cm, find the area of the parallelogram ABCD.

Theorems on Area

Related Questions

The median of a triangle divides it into two:triangles of equal areacongruent trianglesright trianglesisosceles triangles

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The median of a triangle divides it into two:
triangles of equal area
congruent triangles
right triangles
isosceles triangles

The area of given parallelogram is:
AB x BM
BC x BN
DC x DL
AD x DL