Area of Trapezoids Rhombuses and Kites Geometry 7

Area of Trapezoids, Rhombuses, and Kites Geometry 7 -4

Review

Areas

• Area of a Triangle Area

• The Pythagorean theorem In a right triangle, the sum of the squares of the legs of the triangle equals the square of the hypotenuse of the triangle B c a C Theorem b A

• Converse of the Pythagorean theorem If the square of the length of the longest side of a triangle is equal to the sum of the squares of the lengths of the other two sides, then the triangle is a right triangle. B c a C Theorem b A

Converse of Pythagorean

• 45° – 90° Triangle In a 45° – 90° triangle the hypotenuse is the square root of two times as long as each leg Theorem

• 30° – 60° – 90° Triangle In a 30° – 60° – 90° triangle, the hypotenuse is twice as long as the shorter leg, and the longer leg is the square root of three times as long as the shorter leg Theorem

New Material

• Get your supplies • Paper • Scissors • Ruler Investigation

• Construct a trapezoid, and label it as shown • Find the height, by folding • Cut it out Investigation

• Make & label a copy Investigation

• Arrange the two trapezoids to form a figure for which you already know the formula for the area Investigation

• Arrange the two trapezoids to form a figure for which you already know the formula for the area Investigation

• Trapezoid Area Conjecture The area of a trapezoid is given by the formula A = ½ (B 1 + B 2) x H, where A is the area, B 1 and B 2 are the lengths of the two bases, and H is the height of the trapezoid Conjecture

Example

Example

Example

Sample Problems

• Get your supplies • Paper • Scissors • Ruler Investigation

• Cut out a large kite (folding the paper first will make this easy) Investigation

• Clearly mark and label each diagonal d 2 d 1 Investigation

• Cut the kite into pieces, and arrange to make a shape with a known area d 2 d 1 Investigation

• Kite Area Conjecture The area of a kite is given by the formula A = ½ d 1 x d 2 where A is the area, and d 1 and d 2 are the diagonals of the kite Conjecture

• Rhombus • We previously calculated the area of a parallelogram, is there an easier formula for the area of a rhombus? Investigation

Theorems

Practice

Practice

Practice

Sample Problems

Sample Problems

Sample Problems

Practice

Practice

Practice

Practice

Sample Problems

Sample Problems

Practice

Practice

Practice

• Pages 376 – 379 • 1 – 4, 11, 13 – 20, 22, 29, 34 – 37, 48, 49, 50 Homework