Question

Hi I need help please

Answer 1

Answer/Step-by-step explanation:

Recall: if two figures are similar, we know that the ratio of their areas = the square of the ratio of their corresponding sides

Apply this knowledge to solve the problems given.

✔️Problem 1 (4-sided polygon):

Let the missing area be x cm²

Therefore,

$\frac{x}{9} = \frac{8^2}{4^2}$

$\frac{x}{9} = \frac{64}{16}$

$\frac{x}{9} = 4$

Multiply both sides by 9

x = 9*4

x = 36 cm²

✔️Problem 2 (3-sided polygon):

Let the missing area be y cm²

Therefore,

$\frac{y}{240} = \frac{8^2}{32^2}$

$\frac{y}{240} = \frac{64}{1,024}$

$\frac{y}{240} = \frac{1}{16}$

Multiply both sides by 240

y = ¹/16 × 240

y = 15 cm²

✔️Problem 3 (5-sided polygon):

Let the missing area be z cm²

Therefore,

$\frac{z}{40} = \frac{3^2}{2^2}$

$\frac{z}{40} = \frac{9}{4}$

Multiply both sides by 40

$z = \frac{9}{4} * 40$

$z = \frac{9}{1} * 10$

z = 90 cm²