IBPS Sample Mensuration Questions

Dear Reader,
Below are three problems based on the measures of parallelogram, triangle and rectangle

Question1

The base of a rectangle is 14 units and the height is 13 units. What will be the area of the right-angled triangle constructed on the same base and height?
a)90 b)91 c)92 d)93

Answer: b)91

Solution:

We know that, "The area of the right-angled triangle in a rectangle = 1/2 x the area of the rectangle "

Now, 1/2 x the area of the rectangle = 1/2 x base x height

1/2 x 14 x 13 = 7 x 13 = 91 squareunits.

Hence the answer is 91.

Question2

The base of a parallelogram is 36 units and the area of the isosceles triangle constructed on the same base between the parallel lines of the parallelogram is 378 square units. Then the vertical distance between the parallel lines is :
a)21 b)25 c)33 d)24

Answer: a)21

Solution:

Given that the base of the isosceles triangle is the base of the parallelogram = 36 units.
And the isosceles triangle is constructed between the parallel lines of the parallelogram. Then, the altitude of that triangle becomes the vertical distance between the parallel lines.
i.e., we have to find the altitude of that triangle

Therefore "The area of the triangle = 1/2 x the area of the parallelogram "
And The area of the triangle = 1/2 x base x altitude = 378 square units

1/2 x 36 x altitude = 378
altitude = 378 / 18 = 21 units.

Hence the answer is 21.

Question3

A triangle with altitude h1 and a parallelogram with altitude h2 are constructed on the same base such that their areas are equal. Then the relationship between h1 and h2 is ;
a)h1=2h2 b)2h1=h2 c)h1=3h2 d)none of these

Answer: a)h1=2h2

Solution:

Given that the base and the area of the triangle and parallelogram are same.
Let it be b.
The altitude of the triangle = h1
The altitude of the parallelogram = h2

The area of the triangle = 1/2 x b x h1
And The area of the parallelogram = b x h2

Therefore, 1/2 x b x h1 = b x h2
1/2 x h1 = h2
h1 = 2h2
Hence the answer is option a.


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