Question

The triangles are similar. The area of the larger triangle is 200 cm².

What is the area of the smaller triangle?


12.5 cm²

50 cm²

100 cm²

200 cm²

Answer 1

Formula to find Area of a triangle is

A=(height×base)/2

base of bigger triangle is=64cm^2

base of smaller triangle is=16cm^2

Area of bigger triangle is =200cmCm^2

area of smaller triangle=?

we imagine

height = base

then area of bigger trianglewillbe=64*64/2=2048

and area of smallertriangle will be=16*16/2==128

but we are given thatarea of bigger triangle is 200

when we divide 2048/10

it approximately gives 200

similarly when we divide 128/10

it approximately gives 12.5cm^2

hence area of smaller triangle is 12.5cm^2

Answer 2

The correct answer option is 12.5 cm
`^2`.

Explanation:

We are given two triangles that are similar with one of the corresponding sides with known values.

The ratio of the corresponding sides of the smaller triangle to the larger triangle is
`(16)/(64) =(1)/(4)`. So the ratio between the areas of these triangles will be
`(1)/(4^2) =(1)/(16)`.

If the area of the larger triangle is 200 cm
`^(2)` then the area of the smaller triangle will be =
`(1)/(16) *200=12.5`.

Therefore, the area of the smaller triangle is 12.25 cm
`^2`.