Question

1. the polygons are similar. find the area of the other figure.

a) old
4 cm
$a = 10\\,cm^{2}$
new
12 cm
b) old
4 in.
new
20 in.
$a = 100\\,in^{2}$

Explanation:

Step1: Find scale factor (a)

$\text{Scale factor} = \frac{12}{4} = 3$

Step2: Area ratio = scale factor²

$\text{Area ratio} = 3^2 = 9$

Step3: Calculate new triangle area

$\text{New area} = 10 \times 9 = 90$

Step4: Find scale factor (b)

$\text{Scale factor} = \frac{20}{4} = 5$

Step5: Area ratio = scale factor²

$\text{Area ratio} = 5^2 = 25$

Step6: Calculate old rectangle area

$\text{Old area} = \frac{100}{25} = 4$

Answer:

a) $90 \text{ cm}^2$
b) $4 \text{ in}^2$