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Exploring Areas: Triangles, Parallelograms, and Trapezoids

This lesson focuses on developing and applying formulas for calculating the area of triangles, parallelograms, and trapezoids. Students will begin with warm-up problems that involve solving for dimensions using perimeter formulas. They will learn key concepts, including the definitions of base, altitude, and height for these shapes. Activities include drawing triangles and deriving areas, followed by practical examples and exercises. Homework will reinforce understanding with targeted problems on pages 308-309.

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Exploring Areas: Triangles, Parallelograms, and Trapezoids

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  1. 5.2 Area of Triangles, Parallelograms, & Trapezoids Objectives: Develop & apply formulas for the area of triangles, parallelograms, & trapezoids. Warm-Up: The length of the rectangle is 4 inches less than 3 times the width. The perimeter is 40 inches. Find the length and the width.

  2. Collins Writing: Draw a right triangle, how do you think we could determine the area if we only knew the length of the legs? ________________________________ ________________________________ ________________________________ 3 lines 2 minutes

  3. Parts of a Triangle: • Base: Any side of a triangle • Note-for each possible choice of the base of a triangle, there is a corresponding altitude and height • Altitude: a perpendicular segment from a vertex • to a line containing the base of the triangle. • Height: the length of the altitude • altitude • base

  4. The area of a triangle can be found by multiplying the base by one half of the height(altitude) Note: the height must be PERPENDICULAR to the BASE!!! Area =

  5. 35in 29in 21in 48in Area = ? Area = ?

  6. The base of one of the triangles in the pinwheel is 4 cm, the area is 14 cm2, what is the height of one triangle?

  7. Parts of a Parallelogram: • Base: Any side of a parallelogram • Altitude: a perpendicular segment from a line containing the base to a line containing the side opposite the base. • Height: the length of the altitude • base • altitude • base

  8. Parts of a Trapezoid: • Bases: the two parallel sides of a trapezoid • Legs: the two non-parallel sides of a trapezoid • Altitude: a perpendicular segment from a line containing one base to a line containing the other base. • Height: the length of the altitude • base • altitude • base

  9. Example: • Use the diagram and measurements given below to find the areas of the indicated figures. • ∆VWZ = ______ • 9 • W • X • ∆WXY = ______ • 10 • 17 • 8 • VWXY = ______ • Z • Y • 6 • V • WXYz = ______

  10. B A C 2 HSPA questions of the day: ABC is an isosceles triangle. AB BC and m<ABC = BAC = A. 26o B. 64o C. 77o D. 154o m<2 = A. 26o B. 154o C. 72o D. 103o

  11. Homework: • Pages 308-309; Numbers 10-30

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