4/10 – 4/11 Outcomes You will be able to find the areas of squares, rectangles, parallelograms and triangles. You will be able to find the areas of trapezoids, kites, and rhombuses. Announcements- – Haiku Page is up! It has the Study Guide answer key. Use your SG to study for assessment! – See posted OH and SAS.
BellWork (Skill 48) Use the parallelogram DEFG to answer the questions: If DH = 9.5, find FH and DF. IF m GDE = 65 degrees, Find m EFG and m DEF. Find the perimeter of DEFG. 10 H G F D E 12
6.7 Areas of Triangles and Quadrilaterals Area of a Square S S Area = S 2
Area of a Rectangle b h Area = bh
Area of a Parallelogram Area = h b bh
Area of a Triangle b h Area = ½ bh
Where does the area of a parallelogram come from? It comes from the area of a rectangle with the same base and height. b h
Where does the area of a triangle come from? b h h It comes from the area of half of a parallelogram with the same base and height.
Area Congruence Postulate If two polygons are congruent, then they have the same area. Area Addition Postulate The area of a region is the sum of the areas of its non-overlapping parts.
Example 1 1. Find the area of the triangle. A = ½ (10)(12) = 60 square units
Example 2 Find the base of a triangle that has an area of 48 square feet and a height of 3 feet. 3 b 48 sq.ft. = ½ (3)(b) b = 32
Example 3 and 4 Give them a try!
Area of a Trapezoid The area of a trapezoid is one half the product of the height and the sum of the bases. h b2b2 b1b1 Area = ½ h (b 1 + b 2 ) b = (b 1 + b 2 ) 2 b
Where does the area of a trapezoid come from? It also comes from a rectangle. The number used for the Base is the average of the two bases of the trapezoid.
Area of a Kite and a Rhombus Area = ½ d 1 d 2 d2d2 d1d1
Where does the area of a kite come from? The kite takes up half of the Area of a rectangle whose Dimensions are equal to The diagonals of the kite.
Example 1 1. Plot the kite ABCD using A(0,5), B(3,6), C(6,5), and D(3,2). What is the area? Diagonal 1 = 4 Diagonal 2 = 6 Area = 12 sq. units