Geometry unit 1.8
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This document defines geometric shapes and provides formulas to calculate perimeter and area. It defines perimeter as the length of the edge and area as the space within a 2D shape. Formulas are provided for calculating perimeter and area of squares, rectangles, triangles, and circles. An example shows calculating the perimeter and area of a rectangle. Another example uses the distance formula to find the sides of a triangle and then calculates its perimeter and area.
Geometry unit 1.8
- 2. Perimeter - The length of the edge of an object in the plane. Area - The space in the plane defined by an 2 dimensional object.
- 3. Square - side length x Perimeter – 4x x Area – x 2 x x x
- 4. Rectangle - length l and width w Perimeter = 2 l + 2 w w Area = l * w l l w
- 5. Triangle – sides a, b, and c Height - h Perimeter = a + b + c Area = ½hb
- 6. Triangle – sides a, b, and c Height - h Perimeter = a + b + c Area = ½hb
- 7. Circle – Radius r Circumference = 2pr or Area = pr2 dp
- 8. A rectangle of length 4.5 m and width of 0.5 m
- 9. A rectangle of length 4.5 m and width of 0.5 m P = 2(4.5) + 2(0.5) P = 9 + 1; so 10m Area (4.5)(0.5) = 2.25 m2
- 10. A triangle defined by H( -2, 2), J( 3, - 1) and K( - 2, - 4) Find the side by the distance formula ( ) ( )2 1 2 2 1 2 x - x + y - y
- 11. HJ = JK = HK = (3 - (-2))2 + (-1- 2)2 (3 - (-2))2 + (-1- (-4))2 (- 2 - (-2))2 + (2 - (-4))2 = 34 = 34 = 36 34 34 2 34 Perimeter is + + 6 = 6 +
- 12. We need to graph the triangle. (- 2, 2) The distance from ( -2,- 1) to (3, - 1) is 5 (3 ,-1) (-2, -1) (- 2, - 4)
- 13. We need to graph the triangle. (- 2, 2) The distance from ( -2,- 1) to (3, - 1) is 5 ( - 2, 2) to (- 2, 4) is 6 (3 ,-1) Area ½(6)(5) = 15 (-2, -1) (- 2, - 4)
- 14. You need a 2 foot walkway around a pool. The pool is 16 feet by 8 feet rectangle. What is the area of the walkway? What formula do we need?
- 15. You need a 2 foot walkway around a pool. The pool is 16 feet by 8 feet rectangle. What is the area of the walkway? What formula do we need? Rectangle Area We have two rectangles, one inside another.
- 16. Write out the verbal model Pool and walkway minus the pool will give us the walkway. 16 ft + 2ft + 2ft 8ft + 2ft + 2ft
- 17. Pool and walkway - the pool = walkway. (16 + 2 + 2)(2 + 8 + 2) – (16)(8)
- 18. Pool and walkway - the pool = walkway. (16 + 2 + 2)(2 + 8 + 2) – (16)(8) (20)(12) – (16)(8) = walkway 240 – 128 = walkway 112 ft2 is the walkway
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