Question

1.construct a parallelogram ABCD and parallelogram ABEF where AB is equals to 8 cm and the altitude of a parallelogram is 3 cm 2. prove that parallelogram ABCD has the same area as parallelogram ABEF 3. prove that triangle ABC is half the area of parallelogram ABCD

Answer 1

3. area of triangle abc is half of area of parellogram because same base b/w same parell
2.

Answer 2

Area of Parallelogram ABCD = ABEF 24 cm²  , Area of   ΔABC  = (1/2)Area of Parallelogram ABCD

Step-by-step explanation:

Area of a parallelogram = Side * (perpendicular distance between sides)

Side = 8 cm

Altitude = perpendicular distance between sides = 3 cm

Area of Parallelogram ABCD = 8 * 3  = 24 cm²

Parallelogram has opposite sides equal

AB = CD

AB = EF

=> CD = EF = 8 cm

Area of Parallelogram ABEF = 8 * 3  = 24 cm²

ΔBAC & ΔDCA

AC = AC  common

AB = CD

BC = DA

=> ΔBAC ≅ ΔDCA

=> Area of   ΔBAC =  Area of   ΔDCA

Area of   ΔBAC  +  Area of   ΔDCA =Area of Parallelogram ABCD

=> Area of   ΔBAC  = (1/2)Area of Parallelogram ABCD

Area of   ΔABC  = (1/2)Area of Parallelogram ABCD

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