Perimeter, Lines, & Angles

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Presentation transcript:

Perimeter, Lines, & Angles GHSGT Review Perimeter, Lines, & Angles

Perimeter Perimeter is defined as the distance around a figure You can find perimeter for a polygon by adding its side lengths The perimeter of a circle is called its circumference, using the formula C = πd, where d is the length of the diameter

Quadrilaterals Here are the 4-sided figures you need to be familiar with: Rectangle Square Parallelogram Trapezoid

Polygons These are some important polygons; memorize the number of sides each one has: Triangle – 3 sides Pentagon – 5 sides Hexagon – 6 sides Octagon – 8 sides

Regular Polygons A polygon is “regular” if it has equal side lengths and equal angle measures. A regular triangle would have each angle measuring 60o, because 180 ÷ 3 = 60 60o 7 cm 7 cm 60o 60o 7 cm

Example Find the perimeter of the pentagon shown: The perimeter is the sum of its side lengths P = 3 + 3 + 3 + 3 + 3 = (3)(5 sides) = 15 in. 3 in 3 in 3 in 3 in 3 in

Example Q: A regular hexagon has a perimeter of 72 feet. What is the length of each of its sides? A: Regular means that all sides are equal, so 72 ÷ 6 congruent sides = 12 feet each

Circumference You saw before that C = πd to find the perimeter of a circle This circle has a radius of 3 cm To find its circumference, Double the radius to get that its diameter is 6cm, then C = (3.14)(6) = 18.84 cm 3 cm

1. The perimeters of the two triangles are equal 1. The perimeters of the two triangles are equal. What is the value of x? A. 4 cm B. 6 cm C. 8 cm D. 10 cm 6 cm x 10 cm 8 cm 10 cm 8 cm

2. A hexagon has a perimeter of 25 2. A hexagon has a perimeter of 25. Five of its sides are 3, 3, 4, 6, and 6. What is the length of the remaining side? A. 2 B. 3 C. 4 D. 5

3. The regular hexagon shown here has the same perimeter as a square with a side of 18 inches. How long is each side of the hexagon? A. 10 inches B. 12 inches C. 24 inches D. 72 inches

4. Jeffrey has an irregularly shaped backyard, as shown 4. Jeffrey has an irregularly shaped backyard, as shown. What is the perimeter of his backyard? A. 170 feet B. 180 feet C. 200 feet D. 300 feet 40 ft 60 ft 60 ft 40 ft 100 ft

5. The circumference of the circle below is 31. 4 inches 5. The circumference of the circle below is 31.4 inches. Find its diameter. A. 3.2 inches B. 5 inches C. 10 inches D. 98.6 inches C = 31.4 inches

Solutions 1. D – The perimeter of the first triangle is 26. To get x, subtract the sum of the two sides of the second triangle from this number. 2. B – Add the five sides of the hexagon, and then subtract this number from the perimeter of 25 that was given. 3. B – The perimeter of the square is (18)(4 sides) = 72. Then divide 72 by 6 sides to get the side length of the hexagon.

Solutions, continued 4. D – Add up all of the sides to get that his backyard has perimeter 300 feet. 5. C – Use the formula C = πd to substitute: 31.4 = (3.14)(d) Then divide the 3.14 from both sides to find that d = 10 inches.