QUIZ REVIEW Interior Angle Measures Changes in Dimension of Perimeter and Area Surface Area
1 Using (n-2)180, find the sum of the interior angle measures of the given polygon: hexagon Show all work.
ANSWER: hexagon – 6 sides (6-2)180 4(180) 720⁰
2 Suppose the side lengths of the parallelogram below are multiplied by ⅓. What effect would this have on the perimeter? Justify your answer.
ANSWER: Original Perimeter: 12 + 9 + 12 + 9 = 42 inches New Perimeter: 4 + 3 + 4 + 3 = 14 inches Because the sides are ⅓ times the original, then the new perimeter is ⅓ times the original perimeter.
3 Find the missing angle measure for the triangle to the right. Show all work.
ANSWER: 50 + 30 = 80 180 – 80 = 100 100⁰
4 The measures of the angles of triangle XYZ are in the ratio 3:3:6. What are the measures of the angles? Show all work.
45⁰ 90⁰ work: ANSWER: Ratio: 3:3:6 Add 3 + 3 + 6 3 + 3 + 6 = 12 180 ÷ 12 (to find one measure) One measure is 15⁰ 3(15) = 45⁰ 6(15) = 90⁰ ANSWER: 45⁰ 90⁰
5 Find the surface area of the rectangular prism. front and back top and bottom two sides
SA = 800 in2 ANSWER: SURFACE AREA: Top: 15 • 10 = 150 Bottom: 15 • 10 = 150 Front: 15 • 10 = 150 Back: 15 • 10 = 150 Side 1: 10 •10 = 100 Side 2: 10 •10 = 100 SA = 800 in2
6 A rectangle measures 4 feet by 8 feet. Suppose the side lengths are multiplied by 2.5. What effect would this have on the area? Justify your answer.
ANSWER: Original Area: New Area: 4 8 = 32 feet2 10 20 = 200 feet2 Because the side lengths increased 2.5 times, the new area is 2.52 = 2.5 2.5 OR 6.25 times larger than the original area.
7 The soccer ball below consists of repeating pentagons and hexagons. Find the measure of one interior angle of a pentagon. Use (n-2)180. Show all work.
ANSWER: (5 – 2)180 (3)180 540 ⁰ 540 ÷ 5 (to find one angle measure) 108⁰
8 Find the missing angle measure for the triangle to the right. Show all work.
ANSWER: 75 + 60 = 135 180 – 135 = 45 45⁰
9 CARPENTRY Bryan is sanding a set of speaker boxes that he built for his room. What is the surface area of each box? SHOW ALL WORK
Surface Area: Front: 1.1 • 4.6 = 5.06 Back: 1.1 • 4.6 = 5.06 ANSWER: Surface Area: Front: 1.1 • 4.6 = 5.06 Back: 1.1 • 4.6 = 5.06 Top: 1.1 • 2.2 = 2.42 Bottom: 1.1 • 2.2 = 2.42 Side 1: 4.6 • 2.2 = 10.12 Side 2: 4.6 • 2.2 = 10.12 SA = 35.2 ft2
10 The measures of the angles of triangle RST are in the ratio 2:4:9. What are the measures of the angles? Show all work.
24⁰ 48⁰ 108⁰ work: ANSWER: Ratio: 2:4:9 Add 2 + 4 + 9 2 + 4 + 9 = 15 180 ÷ 15 (to find one measure) One measure is 12⁰ 2(12) = 24⁰ 4(12) = 48⁰ 9(12) = 108⁰ ANSWER: 24⁰ 48⁰ 108⁰