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

Review

Areas

Area Area of a Triangle

Theorem 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 A C b B a c

Theorem 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. A C b B a c

Converse of Pythagorean

Theorem 45° – 45° – 90° Triangle In a 45° – 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

New Material

Investigation 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

Conjecture 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

Example

Sample Problems

Investigation 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 d1 d2

Investigation Cut the kite into pieces, and arrange to make a shape with a known area d1 d2

Conjecture 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

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

Theorems

Practice

Sample Problems

Practice

Sample Problems

Practice

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