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PROPERTIES OF QUADRILATERALS QUADRILATERALS Two-dimensional, closed shape Four straight sides and four angles Sum of angles: 360⁰ Diagonals AC, BD Line segment from one vertex to the opposite vertex Seven types of quadrilaterals PARALLELOGRAM Opposite sides are parallel & equal Opposite angles are equal TYPES OF PARALLELOGRAMS Rectangle Parallelogram All angles are 90⁰ Square Parallelogram All angles are 90⁰ All sides are equal in length Rhombus Parallelogram Opposite angles are equal, do not have to be 90⁰ All sides are equal in length TRAPEZOID One pair of opposite sides are parallel A “regular” trapezoid: non-parallel sides ARE equal base angles are equal Regular trapezoid http://www.math.com/school/subject3/lessons/S3U2L3DP.html OTHER QUADRILATERALS Irregular quadrilaterals No specifications Kite Two pairs of adjacent sides are equal in length One pair of opposite angles (the ones that are between the sides of unequal length) are equal in size. One diagonal bisects the other. Diagonals intersect at right angles. CLICKER QUESTION #1 What is the measure of the missing angle? A. 115 ⁰ B. 45 ⁰ C. 65 ⁰ D. 125 ⁰ 115⁰ 65 ⁰ X 115 ⁰ CLICKER QUESTION #2 Which of the following is not true? A. The diagonals of a rhombus are congruent. B. The diagonals of a rectangle are congruent. C. The four sides of a rhombus are congruent. D. The rectangle has 4 right angles. E. A rhombus is a parallelogram. AREA OF QUADRILATERALS Area Number of squares required to cover the surface Be is measured in square units consistent with units Example: If a rectangle is 6 inches wide and 4 feet long, what is the area? Solution: Must convert units to make both measurements consistent. 6 inches = ½ feet ½ ft x 4 ft = 2 ft² Area = 2 ft² AREA OF QUADRILATERALS Type of Quadrilateral Area Formula Parallelogram A = bh Rectangle A = bh Square A = s² Rhombus A = bh Trapezoid A = (1/2)h(b1 + b2) Kite A = (1/2)(d1*d2) Irregular Break into parts & add Key: b – base h – height s – side b1/b2 – base1/base2 d1/d2 – diagonal1/diagonal2 EXAMPLE - FIND AREA OF QUADRILATERAL 6cm 4cm 9cm A = (1/2)h(b1 + b2) = (1/2)(4)(9 + 6) = (1/2)(60) = 30 cm ² CLICKER QUESTION #3 What is the area of the parallelogram? A. 50 cm² B. 60 cm² C. 17 cm² D. 22 cm² CLICKER QUESTION #4 The area of a rhombus is 64 in² and the base is 16 in. Find the height. A. 4 in² B. 1024 in C. 80 in² D. 4 in COMPLETE WORKSHEET IN PAIRS PAIRS #1 A quadrilateral has four sides of equal length and the diagonals are not congruent. Each side is 5 cm in length and the distance between parallel sides is 7 cm. Determine what type of quadrilateral this is and use the corresponding formula to find the area. A. 12 cm² B. 35 cm² C. 25 cm² D. 20 cm² PAIRS #2 The area of a square is 169 square feet. What is the length of each side? A. 42.25 ft B. 84.5 ft C. 13 ft D. 14 ft PAIRS #3 The area of a rectangle is 56 in² and the base is 8 in. Find the height. A. 8 in² B. 448 in C. 448 in² D. 7 in PAIRS #4 Find the missing angle: 115⁰ x A. 45⁰ B. 65⁰ C. 95⁰ D. 115⁰ PAIRS #5 The Smith family has a rectangular backyard with a base of 18 yards and a height of 11 yards. They want to put new grass in the whole backyard; however, there is a square sandbox with sides of 3 yards each in the yard. How many square yards of new grass will they need? (hint: they do not need grass to cover the sandbox) yard A. 55 yd² B. 49 yd² C. 195 yd² D. 189 yd² sandbox ANSWER #1 What is the measure of the missing angle? A. 115 ⁰ B. 45 ⁰ C. 65 ⁰ D. 125 ⁰ What method did you use to solve for the answer? ANSWER #2 Which of the following is not true? A. The diagonals of a rhombus are congruent. B. The diagonals of a rectangle are congruent. C. The four sides of a rhombus are congruent. D. The rectangle has 4 right angles. E. A rhombus is a parallelogram. ANSWER #3 What is the area of the parallelogram? A. 50 cm² B. 60 cm² C. 17 cm² D. 22 cm² ANSWER #4 The area of a rhombus is 64 in² and the base is 16 in. Find the height. A. 4 in² B. 1024 in C. 80 in² D. 4 in PAIRS – ANSWER #1 A quadrilateral has four sides of equal length and the diagonals are not congruent. Each side is 5 cm in length and the distance between parallel sides is 7 cm. Determine what type of quadrilateral this is and use the corresponding formula to find the area. A. 12 cm² B. 35 cm² C. 25 cm² D. 20 cm² PAIRS – ANSWER #2 The area of a square is 169 square feet. What is the length of each side? A. 42.25 ft B. 84.5 ft C. 13 ft D. 14 ft PAIRS – ANSWER #3 The area of a rectangle is 56 in² and the base is 8 in. Find the height. A. 8 in² B. 448 in C. 448 in² D. 7 in PAIRS – ANSWER #4 Find the missing angle: 115⁰ x A. 45⁰ B. 65⁰ C. 95⁰ D. 115⁰ PAIRS – ANSWER #5 The Smith family has a rectangular backyard with a base of 18 yards and a height of 11 yards. They want to put new grass in the whole backyard; however, there is a square sandbox with sides of 3 yards each in the yard. How many square yards of new grass will they need? (hint: they do not need grass to cover the sandbox) yard A. 55 yd² B. 49 yd² C. 195 yd² D. 189 yd² sandbox