Question

remember: perimeter is defined as the distance around a 2d figure. - usually, the perimeter is found by adding the lengths of all the sides of the figure. - the length around a circle is called the circumference and has a unique formula. area is defined as the space inside a 2d figure. formulas: rectangle/square: p = 2l + 2w or p = 4s, a = l × w; triangle: p = a + b + c, a = \frac{1}{2}bh; circle: c = 2\pi r, a = \pi r^{2}. problem set 12 find the area and perimeter/circumference of each of the following figures. round your answers to the nearest hundredth.

Explanation:

Step1: Calculate rectangle's perimeter

For the rectangle with length $l = 7.6$ in and width $w = 5$ in, use the formula $P=2l + 2w$.
$P=2\times7.6+2\times5=15.2 + 10=25.2$ in

Step2: Calculate rectangle's area

Use the formula $A=l\times w$.
$A=7.6\times5 = 38$ in²

Step3: Calculate triangle's perimeter

For the triangle with sides $a = 5.3$, $b = 6.2$, $c = 7.8$, use the formula $P=a + b + c$.
$P=5.3+6.2+7.8=19.3$

Step4: Calculate triangle's area

Use the formula $A=\frac{1}{2}bh$. Here base $b = 7.8$ and height $h = 4.2$.
$A=\frac{1}{2}\times7.8\times4.2=16.38$

Step5: Calculate circle's circumference

For the circle with radius $r = 8.2$, use the formula $C = 2\pi r$.
$C=2\times\pi\times8.2\approx2\times3.14\times8.2 = 51.496\approx51.50$

Step6: Calculate circle's area

Use the formula $A=\pi r^{2}$.
$A=\pi\times(8.2)^{2}=3.14\times67.24 = 211.2236\approx211.22$

Step7: Calculate square's perimeter

For the square with side $s = 8.9$, use the formula $P = 4s$.
$P=4\times8.9=35.6$

Step8: Calculate square's area

Use the formula $A=s^{2}$.
$A=(8.9)^{2}=79.21$

Answer:

1. Rectangle: Perimeter = 25.20 in, Area = 38.00 in²
2. Triangle: Perimeter = 19.30, Area = 16.38
3. Circle: Circumference = 51.50, Area = 211.22
4. Square: Perimeter = 35.60, Area = 79.21