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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
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Solution
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
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