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How much paint do we need to paint all the rooms in our house? kitchen bedroom TV room Square Area = s2 (s = side length) Rectangle Area = lw (l = length and w = width) Triangle Area = ½bh (b = base and h = height) You can justify the area formula for triangles as follows: The area of a triangle is half the area of a parallelogram with the same base and height. Area of a Parallelogram = bh Area of a Triangle = ½bh Be careful when identifying the height of a triangle! The height is NEVER a side of a triangle unless the triangle is RIGHT. h h h Ex 1: Find the area of.. a. A square whose sides have length 8 cm. 8 cm 8 cm 8 cm 8 cm A = s2 A = 82 A = 64 cm2 b. A rectangle whose length is 5 m and width is 11 m. 5m 11 m 11 m 5m A = lw A = (5)(11) A = 55 m2 c. A triangle whose side lengths are 3 in, 4 in, and 5 in. 5 in 4 in 3 in A = ½ (4)(3) A = ½ (12) A = 6 in2 Ex 2: Find the indicated side length. a. A square with area 256 in2. 16 in 16 in 16 in 16 in A = s2 256 = s2 16 = s b. A rectangle with area 345 ft and length 15 ft. 15 ft 23 ft 23 ft 15 ft A = lw 345 = 15w 23 ft = w c. A triangle with area 12 mm and a base length of 6 mm. 4 mm 6 mm A = ½ bh 12 = ½ (6)h 12 = 3h 4 mm = h Parallelogram Area = bh (b = base and h = height) Trapezoid Area = ½ h (b1 + b2) Rhombus Area = ½d1d2 (d = diagonal) You can justify the area formula for parallelograms as follows: h The area of a parallelogram is the area of a rectangle with the same base and height. Area of Parallelogram = bh Ex 3: Find the area of parallelogram ABCD B C A bh 9 16 E 12 A 16(9) A 144units 2 A 12 D Method 1 Use AB as the base and BE as the height. F Ex 3: Find the area of parallelogram ABCD C B A bh 9 16 E 12 A 12(12) A 144units 2 A 12 D F Method 2 You get the same Use AD as the base and answer. CF as the height. Ex 4: Find the area of trapezoid WXYZ. 1 A h(b1 b2 ) 2 1 Y(2, 5) Z(5, 5) A ( 4)(3 7) 2 1 A ( 4)(10) 2 1 A ( 40) X(1, 1) W(8, 1) 2 A 20units2 Count the blocks for height, base 1, and base 2. Ex 5:The area of a trapezoid is 135 cm2, height is 9, and one bases is 11. Find the other base. 1 A h(b1 b2 ) 2 1 135 (9)(11 x ) 2 270 (9)(11 x ) 270 99 9 x 171 9 x 19cm x Ex 6: Find the area of the rhombus. 9 12 9 12 1 A d1d 2 2 1 A (18)(24) 2 1 A (432) 2 2 A 216units Ex 7: The area of a rhombus is 40 in2 and one of the diagonals is 8 in. Find the other diagonal. 1 A d1 d 2 2 1 40 (8) d 2 2 40 4d 2 10 d 2 Circle Area = r 2 Ex 8: Find the area if the radius 8 3 . A r 8 3 2 A (8 3 ) A (64 3) A 192 2 Leave your answer in terms of pi unless stated otherwise.