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Understanding Areas of Triangles, Rhombi, and Trapezoids in Geometry

This lesson explores the calculations of areas for triangles, rhombi, and trapezoids. Utilizing geometric principles, we derive area formulas from fundamental concepts, focusing on triangles and extending our understanding to trapezoids. The lesson incorporates examples, such as finding areas of given figures and deriving dimensions from area formulas. We conclude with a summary of the learned area formulas and assign practice problems for reinforcement. Unlock the geometric shapes by mastering these area calculations.

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Understanding Areas of Triangles, Rhombi, and Trapezoids in Geometry

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Presentation Transcript

  1. Chapter 10: Exploring Polygons and Area Lesson 10-4: Area of Triangles, Rhombi, and Trapezoids p. 535-538

  2. Review from Previous Class • Refer to the figure below to find each area. • ABCDEF • Shaded part of GHIE • HONMLKJI • The entire figure including the unshaded part of GHIE A B H O L G K N M C D J F E I

  3. Area of a Triangle • If a triangle has an area of A square units, a base of b units, and a corresponding height of h units, then

  4. Example 1 • Find each area. 4 cm 7 cm 5 cm 8 cm h 60º 4 in

  5. Deriving the Area of a Trapezoid • Now, let’s use the formula for area of a triangle to derive the formula for the area of a trapezoid. • Area of a trapezoid RSTU = area of triangle RSU + area of triangle STU R S h T U

  6. Deriving the Area of a Trapezoid • Area of RSTU = area of triangle RSU + area of triangle STU

  7. Area of a Trapezoid • If a trapezoid has an area of A square units, bases of b units, and height of h units, then

  8. Example 2 • Find the height of a trapezoid that has an area of 50 square yards and bases of 8 yards and 12 yards.

  9. Area of a Rhombus • If a rhombus has an area of A square units and diagonals of d1 and d2 units, then

  10. Example 3 • A rhombus with a 20-centimeter diagonal has an area of 300 square centimeters. Find the perimeter of the rhombus

  11. Summary • The following chart summarizes the area formulas that we have learned thus far.

  12. Homework • p. 539 #11-19

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