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,
[tex] \frac{x}{9} = \frac{8^2}{4^2} [/tex]
[tex] \frac{x}{9} = \frac{64}{16} [/tex]
[tex] \frac{x}{9} = 4 [/tex]
Multiply both sides by 9
x = 9*4
x = 36 cm²
✔️Problem 2 (3-sided polygon):
Let the missing area be y cm²
Therefore,
[tex] \frac{y}{240} = \frac{8^2}{32^2} [/tex]
[tex] \frac{y}{240} = \frac{64}{1,024} [/tex]
[tex] \frac{y}{240} = \frac{1}{16} [/tex]
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,
[tex] \frac{z}{40} = \frac{3^2}{2^2} [/tex]
[tex] \frac{z}{40} = \frac{9}{4} [/tex]
Multiply both sides by 40
[tex] z = \frac{9}{4} * 40 [/tex]
[tex] z = \frac{9}{1} * 10 [/tex]
z = 90 cm²
