Two figures have a similarity ratio of 3:7. If the area of the larger figure is 294 cm what is the area of the smaller figure?

Question

Evelyn Arboleda · Accepted Answer

smaller area#=126cm^2# Ratio 7#=294# :.Ratio 3#=3/cancel7^color(red)1 xx cancel294^color(red)42/1# #:.=3*42=126cm^2# check: #:.cancel126^color(red)3/cancel294^color(red)7# #:.3/7= ratio 3:7#

Savannah Aguilar · Answer

undefined If the similarity ratio between the two figures is 3:7, then the ratio of their areas is the square of this ratio, which is (3/7)^2 = 9/49.

Given that the area of the larger figure is 294 cm^2, we can find the area of the smaller figure by multiplying the area of the larger figure by the ratio of their areas:

Area of smaller figure = (Area of larger figure) * (Ratio of areas)
                      = 294 cm^2 * (9/49)
                      = 54 cm^2.

So, the area of the smaller figure is 54 square centimeters.

Noah Atkinson · Answer

undefined If the similarity ratio of two figures is 3:7, then the ratio of their areas is the square of the similarity ratio.

Given that the area of the larger figure is 294 cm², and the similarity ratio is 3:7, we can set up the proportion:

$$ \frac{\text{Area of larger figure}}{\text{Area of smaller figure}} = \left(\frac{\text{larger figure ratio}}{\text{smaller figure ratio}}\right)^2 $$

$$ \frac{294}{\text{Area of smaller figure}} = \left(\frac{7}{3}\right)^2 $$

$$ \frac{294}{\text{Area of smaller figure}} = \left(\frac{49}{9}\right) $$

To find the area of the smaller figure, solve for the area:

$$ \text{Area of smaller figure} = \frac{294 \times 9}{49} $$

$$ \text{Area of smaller figure} = \frac{2646}{49} $$

$$ \text{Area of smaller figure} \approx 54 \, \text{cm}^2 $$

Therefore, the area of the smaller figure is approximately 54 cm².