Question

A triangle with an area of 2/3 cm? is dilated by a factor of 6. What is the area of the dilated triangle? Enter your answer in the box. Do not leave your answer as a fraction.

Answer 1

Answer:

Let A be the area of the dilated triangle.

Given the statement: A triangle with an area of 2/3 cm2 is dilated by a factor of 6.

⇒ Pre-image triangle has an area  = $\frac{2}{3}$ $cm^2$

Scale factor(k) states that the dimension of the Dilated-image is 6 times longer than the dimensions of the pre-image.

i.e,

$k = \frac{\text{Dilation image}}{\text{Pre-image}}$

Substitute the given values to find the value of area of dilated triangle.

$6 = \frac{A}{\frac{2}{3} }$

or

$6 = \frac{3A}{2}$

Multiply both sides by 2 we get;

$12 = 3A$

Divide both sides by 3 we get;

$4 = A$

Therefore, the area of the dilated triangle is, $4 cm^2$