Area

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 ]

3 ft

3 ft

Area: How many square units make up the inside of the object?

Area = 9 ft2

2 cm

4 cm

Area = 8 cm2Area 10 in2

5 in

4 in

Area measures the space in two dimensions.

Area of a Square or Rectangle Area = (length)(width)

A = l • w

3 ft

3 ft

A = l • w

= 3 • 3

Area = 9 ft2

2 cm

4 cm

A = l • w

= 2 • 4

Area = 8 cm2

Sample Test Problem #1One side of a square has a length of 1.5 feet. What is the

area of the square?

a) 2.25 ft2

b) 2.50 ft2

c) 3 ft2

d) 6 ft2

Area = (length)(width)

A = l • w

= 1.5 • 1.5

= 2.25 ft2

Answer: a

Sample Test Problem #2Juan 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?

a) 25 ft2

b) 50 ft2

c) 150 ft2

d) 325 ft2

Area = (length)(width)

A = l • w

= 10 • 15

= 150 ft2

Answer: c

Area of a ParallelogramArea = (base)(height)

A = b • h

= 7 • 4

= 28 in2

7 in

4 in

8 cm

6 cm

Area = (base)(height)

A = b • h

= 6 • 8

= 48 cm2

Sample Test Problem #3

Which parallelogram has an area of 10 square centimeters?

a) Base =5 ; Height = 5

b) Base = 2 ; Height = 5

c) Base = 20 ; Height = 2

d) Base = 15 ; Height = 5

Area = (base)(height)

A = b • h

= 2 • 5

= 10 cm2

Answer: b

A = ½ (b)(h)

= ½ (4)(5)

Area = 10 in2

5 in

4 in

Area of a TriangleArea = ½ (base)(height)

A = ½ (b)(h)

3 m

7 m

A = ½ (b)(h)

= ½ (7)(3)

= 10.5 m2

Sample Test Problem #4What is the area of the figure below?

a) 32 m2

b) 48 m2

c) 96 m2

d) 160 m2

6 m 10 m

16 m

A = ½ (b)(h)

= ½ (16)(6)

= 48 m2

Area of a TrapezoidArea = +

Area = ½ (b1)(h) + ½(b2)(h)

Area = ½ (b1+b2)h

1

2h

b1

b2

Trapezoid

10 cm

6 cm

4 cm

Area = ½ (b1+b2)h

= ½ (10 + 6)4

= ½ (16)(4)

Area = 32 cm2

3mm 8mm

2mm

Area = ½ (b1+b2)h

= ½ (3+8)2

= ½ (11)(2)

Area = 11 mm2

Sample Problem #5What is the area of the figure below?

a) 16.5 in2

b) 23.5 in2

c) 42 in2

d) 63 in2

Area = ½ (b1+b2)h

= ½ (7 + 4)3

= ½ (11)(3)

Area = 16.5 in2

Answer: a

3 in

7 in

4 in

5 in4.5 in

Area of a Circle

2rA 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

•radius

Circle

5 cm

5.78

)25)(14.3(

)5)(14.3( 2

2

rA

cm2

Area (Pi)(radius)2

Sample Problem #6

What is the approximate area of a circle that has a radius of 6 millimeters?

a) 9.14 mm2

b) 18.84 mm2

c) 37.68 mm2

d) 113.04 mm2

04.113

)36)(14.3(

)6)(14.3( 2

2

rA

Answer: d

Sample Problem #7

What is the approximate area of the circle below?

a) 23.14 cm2

b) 62.8 cm2

c) 125.6 cm2

d) 314 cm2

20 cm

314

)100)(14.3(

)10)(14.3( 2

2

rA

Answer: d

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