Question

Explain the area of the parallelogram as sum of the areas of the two triangles.

Accepted Answer

The area $A$ of a parallelogram $A B C D$ is given by the product of its base $b$ and the height $h$ . The height of a parallelogram is the perpendicular distance between its two parallel sides. Thus, $A = b \times h$ .

The area of a triangle is half of the product of its base and its height.

Now, if we join its diagonal $B D$ , it divides the parallelogram $A B C D$ into two congruent triangles of the same base and height as the parallelogram.

We have, $area of A B C D = A B \times h$

Now, $ar (△ A B D) + ar (△ B C D) = \frac{1}{2} \times A B \times h + \frac{1}{2} \times C D \times h$

$= \frac{1}{2} \times A B \times h + \frac{1}{2} \times A B \times h$ [Opposite sides of a parallelogram are equal]

$= 2 \times \frac{1}{2} \times A B \times h = A B \times h = area of A B C D$

So, the area of the parallelogram is the sum of the areas of the two triangles.

Tamil Nadu Board Solutions for Chapter: Measurements, Exercise 1: Think

Tamil Nadu Board Mathematics Solutions for Exercise - Tamil Nadu Board Solutions for Chapter: Measurements, Exercise 1: Think

Questions from Tamil Nadu Board Solutions for Chapter: Measurements, Exercise 1: Think with Hints & Solutions

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