Measure of the space inside a given 2 dimensional area

CAHSEE: Measurement and Geometry MG 2.1 Use formulas routinely for finding the perimeter and area of basic two-dimensional figures and the surface area and volume of basic three-dimensional figures including rectangles, parallelograms, trapezoids, squares, triangles, prisms, and cylinders. [ 3 questions ]

Area: How many square units make up the inside of the object? 2 cm 3 ft 5 in 4 cm 3 ft 4 in Area 10 in2 Area = 9 ft2 Area = 8 cm2 Area measures the space in two dimensions.

Area of a Square or Rectangle Area = (length)(width) A = l • w 2 cm 3 ft 4 cm 3 ft A = l • w = 2 • 4 Area = 8 cm2 A = l • w = 3 • 3 Area = 9 ft2

Sample Test Problem #1 One side of a square has a length of 1.5 feet. What is the area of the square? 2.25 ft2 2.50 ft2 3 ft2 6 ft2 Area = (length)(width) A = l • w = 1.5 • 1.5 = 2.25 ft2 Answer: a

Sample Test Problem #2 Juan is going to put new carpet in the upstairs bedroom. The room is 10 feet by 15 feet. How much carpet will he need to purchase for this room? 25 ft2 50 ft2 150 ft2 325 ft2 Area = (length)(width) A = l • w = 10 • 15 = 150 ft2 Answer: c

Area of a Parallelogram Area = (base)(height) A = b • h = 7 • 4 = 28 in2 4 in 7 in Area = (base)(height) A = b • h = 6 • 8 = 48 cm2 6 cm 8 cm

Sample Test Problem #3 Which parallelogram has an area of 10 square centimeters? Base =5 ; Height = 5 Base = 2 ; Height = 5 Base = 20 ; Height = 2 Base = 15 ; Height = 5 Area = (base)(height) A = b • h = 2 • 5 = 10 cm2 Answer: b

Area of a Triangle Area = ½ (base)(height) A = ½ (b)(h) A = ½ (b)(h) 5 in 3 m 4 in 7 m A = ½ (b)(h) = ½ (4)(5) Area = 10 in2 A = ½ (b)(h) = ½ (7)(3) = 10.5 m2

Sample Test Problem #4 What is the area of the figure below? 32 m2 A = ½ (b)(h) = ½ (16)(6) = 48 m2 10 m 6 m 16 m

Area of a Trapezoid Area = + Area = ½ (b1)(h) + ½(b2)(h) Area = ½ (b1+b2)h b2 2 h 1 b1

Trapezoid Area = ½ (b1+b2)h Area = ½ (b1+b2)h = ½ (3+8)2 = ½ (10 + 6)4 10 cm 3mm 8mm 4 cm 2mm 6 cm Area = ½ (b1+b2)h = ½ (3+8)2 = ½ (11)(2) Area = 11 mm2 Area = ½ (b1+b2)h = ½ (10 + 6)4 = ½ (16)(4) Area = 32 cm2

Sample Problem #5 What is the area of the figure below? 16.5 in2 Area = ½ (b1+b2)h = ½ (7 + 4)3 = ½ (11)(3) Area = 16.5 in2 Answer: a 7 in 3 in 5 in 4.5 in 4 in

Area of a Circle Area = Pi • radius2 Pi ( ) – ratio of the circumference of a circle to its diameter: approximate value = 3.14 radius ( r ) - measure from center of a circle to any side

Circle Area (Pi)(radius)2 5 cm cm2

Sample Problem #6 What is the approximate area of a circle that has a radius of 6 millimeters? 9.14 mm2 18.84 mm2 37.68 mm2 113.04 mm2 Answer: d

Sample Problem #7 What is the approximate area of the circle below? 23.14 cm2 62.8 cm2 125.6 cm2 314 cm2 20 cm Answer: d

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