Question

1. 15.25 m 13.3 m 7 m 30.5 m 14 m p = ____ m
2. 1.7 cm 4 cm 9.3 cm 0.4 cm 0.93 cm r = ____ cm
3. 15 in. 6 in. 18 in. 10 in. 4 in. s = ____ in.
4. 20 m 8 m 36 m 25 m 45 m t = ____ m

Explanation:

Step1: Analyze similar - shaped figures in problem 3

For the two similar - shaped figures in problem 3, we use the property of similar figures where the ratios of corresponding sides are equal.
Let's consider the horizontal and vertical sides. The ratio of the horizontal sides of the two figures is $\frac{30.5}{15.25}=2$. Then, for the vertical sides, we have $\frac{p}{13.3}=2$.

Step2: Solve for $p$

From $\frac{p}{13.3}=2$, we can solve for $p$ by multiplying both sides of the equation by $13.3$. So, $p = 13.3\times2=26.6$ m.

Step3: Analyze similar - shaped figures in problem 4

For the two similar trapezoids in problem 4, the ratio of the non - parallel sides is $\frac{0.4}{4}=\frac{1}{10}$. Then, for the parallel sides, the ratio of the top - parallel sides should be the same. Let the top - parallel side of the smaller trapezoid be $r$. We have $\frac{r}{1.7}=\frac{1}{10}$.

Step4: Solve for $r$

From $\frac{r}{1.7}=\frac{1}{10}$, we multiply both sides by $1.7$ to get $r=\frac{1.7}{10}=0.17$ cm.

Step5: Analyze similar - shaped figures in problem 5

For the two similar pentagons in problem 5, the ratio of the corresponding sides is $\frac{10}{15}=\frac{2}{3}$. Then, for the bottom sides, we have $\frac{s}{18}=\frac{2}{3}$.

Step6: Solve for $s$

Cross - multiply the equation $\frac{s}{18}=\frac{2}{3}$: $3s=18\times2$. Then $s = 12$ in.

Step7: Analyze similar - shaped figures in problem 6

For the two similar polygons in problem 6, the ratio of the corresponding sides is $\frac{45}{36}=\frac{5}{4}$. Then, for the other corresponding sides, we have $\frac{t}{8}=\frac{5}{4}$.

Step8: Solve for $t$

Cross - multiply the equation $\frac{t}{8}=\frac{5}{4}$: $4t=8\times5$. Then $t = 10$ m.

Answer:

$p = 26.6$ m, $r = 0.17$ cm, $s = 12$ in, $t = 10$ m