Question

parallelogram and a triangle have a common base. If area of the triangle is 20cm^2 then find area of a parallelogram (a)20cm^2 (b)40cm^2 (c)10cm^2 (d)400cm^2 ​

Answer 1

Given : a parallelogram and a triangle have a common base  

area of the triangle is 20cm²

To Find : area of parallelogram

(a)20cm^2 (b)40cm^2 (c)10cm^2 (d)400cm^2 ​

Solution:

Area of triangle = (1/2) * base * height

Area of Parallelogram  = base * height

parallelogram and a triangle have a common base  b = b

and  if vertex of triangle  lie of opposite side of parallelogram

Then h will also be common

Then Area of Parallelogram  = 2   (1/2) * base * height

=> Area of Parallelogram  = 2 Area of triangle

=>  Area of Parallelogram  = 2  * 20

=>  Area of Parallelogram  = 40  cm²

If third vertex in not on opposite side of parallelogram / or in line of that

then we can not find any relation.

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Answer 2

SOLUTION

GIVEN

A parallelogram and a triangle have a common base

Area of the triangle is 20 cm²

TO CHOOSE THE CORRECT OPTION

The area of parallelogram

(a) 20 cm²

(b) 40 cm²

(c) 10 cm²

(d) 400 cm²

EVALUATION

Let b cm be the base of the triangle

Since the parallelogram and the triangle have a common base

So base of the parallelogram = b cm

Let h cm be the height of the triangle

Then altitude of the parallelogram = h cm

Then area of the triangle

$\displaystyle \sf{ = \frac{1}{2}bh \: \: {cm}^{2} }$

So by the given condition

$\displaystyle \sf{ \frac{1}{2}bh = 20 }$

$\implies \: \displaystyle \sf{ bh \: \: = 40 }$

So area of the parallelogram

= bh cm²

= 40 cm²

FINAL ANSWER

Hence the correct option is (b) 40 cm²

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