Question

If each side of a triangle is doubled, then its area is __________ times the area of the original triangle.

Answer 1

Let the base of the original triangle be a units and height be b units.

Then, the area of original triangle is $\frac{1}{2}ab$ ...(1)

According to the question,
Each side of a triangle is doubled

Thus, base of the new triangle is 2a units and height is 2b units.

Area of new triangle = $\frac{1}{2}\times 2a\times 2b$
= $\frac{1}{2}\left(4ab\right)$
= $4\times \frac{1}{2}ab$
= 4 × area of original triangle (from (1))


Hence, if each side of a triangle is doubled, then its area is 4 times the area of the original triangle.