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Abcd is a Parallelogram. P is Any Point on Cd. If Ar (δDpa) = 15 Cm2 and Ar (δApc) = 20 Cm2, Then Ar (δApb) = - Mathematics


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


  • 15 cm2

  • 20 cm2

  • 35 cm2

  • 30 cm2

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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 cm


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RD Sharma Mathematics for Class 9
Chapter 14 Areas of Parallelograms and Triangles
Q 6 | Page 60
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