Question

ABCD is a parallelogram. P is any point on CD. If ar (ΔDPA) = 15 cm2 and ar (ΔAPC) = 20 cm², then ar (ΔAPB) =

Options

• 15 cm²

• 20 cm²

• 35 cm²

• 30 cm²

Answer 1

Given: (1) ABCD is a parallelogram

(2) P is any point on CD

(3) Area of ΔDPA = 15 cm²

(4) Area of ΔAPC = 20 cm²

To find: Area of ΔAPB

Calculation: We know that , “If a parallelogram and a a triangle are on the base between the same parallels, the area of triangle is equal to half the area of the parallelogram.”

Here , ΔAPB and ΔACB are on the same base and between the same parallels.

(since AC is the diagonal of parallelogram ABCD, diagonal of a parallelogram divides the parallelogram in two triangles of equal area)

ar (ΔACB ) = ar (ΔAPB) 

ar (ΔACB) = ar (ΔADC) 

ar (ΔACB) = Area of ΔADP + Area of ΔAPC 

                 = 20 +15 

                 = 35 cm²

Area of ΔACB = 35 cm²