Question

1. crafts the quilt pattern includes 32 small triangles. each has a base of 3 in. and a height of 1.5 in. find the amount of fabric used to make the 32 triangles. find the circumference and area of each circle with the given radius or diameter. use the π key on your calculator. round to the nearest tenth. 14. r = 12 m 15. d = 12.5 ft 16. d = 1/2 mi find the area of each of the following. 17. square whose sides are 9.1 yd in length 18. square whose sides are (x + 1) in length 19. triangle whose base is 5 1/2 in. and whose height is 2 1/4 in.

Explanation:

Step1: Recall circle formulas

Circumference $C = \pi d$ or $C = 2\pi r$, area $A=\pi r^{2}$.

Step2: Solve for problem 14

$r = 12$ m. $C=2\pi r=2\pi\times12\approx75.4$ m, $A = \pi r^{2}=\pi\times12^{2}\approx452.4$ m².

Step3: Solve for problem 15

$d = 12.5$ ft. $C=\pi d=\pi\times12.5\approx39.3$ ft, $r=\frac{d}{2}=6.25$ ft, $A=\pi r^{2}=\pi\times6.25^{2}\approx122.7$ ft².

Step4: Solve for problem 16

$d=\frac{1}{2}$ mi. $C=\pi d=\pi\times\frac{1}{2}\approx1.6$ mi, $r=\frac{d}{2}=\frac{1}{4}$ mi, $A=\pi r^{2}=\pi\times(\frac{1}{4})^{2}\approx0.2$ mi².

Step5: Solve for problem 17

For square with side $s = 9.1$ yd, $A=s^{2}=9.1^{2}=82.8$ yd².

Step6: Solve for problem 18

For square with side $s=(x + 1)$ in, $A=s^{2}=(x + 1)^{2}=x^{2}+2x + 1$ in².

Step7: Solve for problem 19

For triangle with $b = 5\frac{1}{2}=\frac{11}{2}$ in and $h=2\frac{1}{4}=\frac{9}{4}$ in, $A=\frac{1}{2}bh=\frac{1}{2}\times\frac{11}{2}\times\frac{9}{4}=\frac{99}{16}=6.2$ in².

Answer:

1. $C\approx75.4$ m, $A\approx452.4$ m²
2. $C\approx39.3$ ft, $A\approx122.7$ ft²
3. $C\approx1.6$ mi, $A\approx0.2$ mi²
4. $A = 82.8$ yd²
5. $A=x^{2}+2x + 1$ in²
6. $A\approx6.2$ in²