Hi I need help please

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,

Multiply both sides by 9

x = 9*4

x = 36 cm²

✔️Problem 2 (3-sided polygon):

Let the missing area be y cm²

Therefore,

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,

Multiply both sides by 40

z = 90 cm²

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4