Question

pre algebra #7
5.)
12 ½ in.
8 ½ in.
6.)
10 in.
9.2 ft.
perimeter =
perimeter =
area =
area =
7.)
4.2 m.
8.)
10 mm.
8 mm.
9 mm.
4 mm.
circumference =
perimeter of triangle =
area =
area =
9.)
22 in.
20 in.
18 in.
24 in.
perimeter =
have
formulas
on page 17
memorized
for the test
before doing the self test,
check your answers to these
9 problems on the bottom of
page 16. if you missed any
of these, see a tutor.
area =

Explanation:

Step1: Convert mixed numbers to improper fractions

For the triangle in problem 5:

• \(12\frac{1}{2}=\frac{12\times2 + 1}{2}=\frac{25}{2}\)
• \(8\frac{1}{2}=\frac{8\times2+1}{2}=\frac{17}{2}\)

Step2: Calculate the perimeter of the triangle in problem 5

Perimeter \(P=a + b + c\)
\(P=\frac{25}{2}+10+\frac{17}{2}\)
\(P=\frac{25 + 17}{2}+10\)
\(P=\frac{42}{2}+10\)
\(P = 21+10=31\) inches

Step3: Calculate the area of the triangle in problem 5

Area \(A=\frac{1}{2}\times base\times height\)
\(A=\frac{1}{2}\times10\times\frac{17}{2}\)
\(A=\frac{170}{4}=\frac{85}{2}=42.5\) square inches

Step4: Calculate the perimeter of the square in problem 6

Perimeter of a square \(P = 4s\) (where \(s\) is the side - length)
\(P=4\times9.2 = 36.8\) feet

Step5: Calculate the area of the square in problem 6

Area of a square \(A=s^{2}\)
\(A=(9.2)^{2}=84.64\) square feet

Step6: Calculate the circumference of the circle in problem 7

Circumference \(C=\pi d\) (where \(d\) is the diameter)
\(C = 3.14\times4.2=13.188\) meters

Step7: Calculate the area of the circle in problem 7

Area \(A=\pi r^{2}\), \(r=\frac{d}{2}=2.1\)
\(A = 3.14\times(2.1)^{2}=3.14\times4.41 = 13.8474\) square meters

Step8: Calculate the perimeter of the triangle in problem 8

Perimeter \(P=a + b + c\)
\(P=10 + 9+4=23\) millimeters

Step9: Calculate the area of the triangle in problem 8

Area \(A=\frac{1}{2}\times base\times height\)
\(A=\frac{1}{2}\times4\times8=16\) square millimeters

Step10: Calculate the perimeter of the triangle in problem 9

Perimeter \(P=a + b + c\)
\(P=22+20 + 24=66\) inches

Step11: Calculate the area of the triangle in problem 9

Area \(A=\frac{1}{2}\times base\times height\)
\(A=\frac{1}{2}\times24\times18=216\) square inches

Answer:

1. Perimeter \( = 31\) in, Area \(=42.5\) in²
2. Perimeter \( = 36.8\) ft, Area \(=84.64\) ft²
3. Circumference \(=13.188\) m, Area \(=13.8474\) m²
4. Perimeter of Triangle \(=23\) mm, Area \(=16\) mm²
5. Perimeter \(=66\) in, Area \(=216\) in²