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,

`(x)/(9) = (8^2)/(4^2)`

`(x)/(9) = (64)/(16)`

`(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,

`(y)/(240) = (8^2)/(32^2)`

`(y)/(240) = (64)/(1,024)`

`(y)/(240) = (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,

`(z)/(40) = (3^2)/(2^2)`

`(z)/(40) = (9)/(4)`

Multiply both sides by 40

`z = (9)/(4) * 40`

`z = (9)/(1) * 10`

z = 90 cm²