Question

Question
1
Question
2
Question
3
A)
Use the formula to determine the area of a regular pentagon with edges measuring 4.5 inches andan apothem measuring 6 inches.
(1 point)
81 in.2
75 in.2
135 in.2
67.5 in.2
A)
A regular hexagon has side lengths of 8 centimeters. What is the exact measure of its apothem?
(1 point)
cm 8 3
–
√
cm 4 3
–
√
6 cm
4 cm
A)
Apply the formula for area of a regular polygon to find the area of a regular hendecagon with sidesthat are 10 centimeters long. Round the answer to the nearest tenth.
(1 point)
1, 873.1 cm2
936.6 cm2
427.9 cm2
1, 020 cm2
Question
4
Question
5
A)
A regular pentagon has a radius of 12 millimeters. What is the measure of each side of thepentagon? Round the answer to the nearest tenth.
(1 point)
22.8 mm
14.1 mm
19.4 mm
12.0 mm
A)
The radius of a regular octagon is 10 centimeters. Identify the calculation that should be used to findthe apothem.
(1 point)
a = 10
sin(22.5°)
a = 10 cos(22.5°)
a = 10
cos(22.5°)
a = 10 sin(22.5°)

Answer 1

Here are the answers with brief work:

1) Area of regular pentagon: A = (1/2)(perimeter)(apothem) = (1/2)(5·4.5)(6) = 67.5 in^2.
Answer: 67.5 in.^2

2) Regular hexagon with side 8: apothem = R cos(30°) and R = side = 8, so a = 8·cos30° = 8·(√3/2) = 4√3 cm.
Answer: 4√3 cm

3) Area of regular hendecagon (n=11, s=10): A = (n s^2)/(4 tan(π/n)) = (11·100)/(4·tan(π/11)) ≈ 936.6 cm^2.
Answer: 936.6 cm^2

4) Regular pentagon, radius (circumradius) R = 12 mm: side s = 2R sin(π/5) = 24·sin36° ≈ 14.1 mm.
Answer: 14.1 mm

5) Radius of regular octagon R =10 cm; apothem a = R cos(π/8) = 10 cos(22.5°).
Answer: a = 10 cos(22.5°)