SQUARE
The area of a square is equal to the length of its side times itself or the side squared. Formula: A=s
2
(figure available in print form)
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1. What is the area of a square whose sides is 23 feet?
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2. Find the area of squares whose sides measure: (a) 15 yd, (b) 42 in. (c) 320 rd., (d) 7,090 ft., (e) 1,760, (f) 0.64 mi., (g) 39.37, (h) 20 1/2 ft, (i) 6 3/8 in., (j) 5 ft. 8 in.
RECTANGLE
To find the area of any rectangle, multiply the measure of the length times the width. Formula: Area= length x width.
(figure available in print form)
1. What is the area of the following rectangle whose measurements are:
(a) length=20 cm
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width=10 cm
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(b) length=15 m
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width=35 m
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(c) length=5 mm
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width=9 mm
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PARALLELOGRAM
To find the area of a parallelogram, multiply the base times the heights. Formula: A = b x h
1. What is the area of the following parallelogram?
(a) base = 400 cm
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height = 24 cm
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A= bxh
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400
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(b) base = 12.5 m
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height = 1.42 m
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A=24x400
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x 24
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(c) base = 14 mm
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height = 7 mm
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A=9600cm
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1600
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800
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Answer:9600cm
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9600cm
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TRIANGLE
The area of a triangle is equal to one half the altitude times the base. Formula: A = 1/2 ab or A = a x b
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2
1. Find the Area of a triangle with an altitude of 26ft. and a base of
17ft.
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A=1/2 ab
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a=26’
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A=1/2x(26x17)
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b=17’
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A=221 sq. ft.
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Answer: 221 sq.ft.
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(figure available in print form)
Find the areas of triangles having the following dimensions.
altitude
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20 in.
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26 1/2 ft.
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4.8yd.
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base
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15 in.
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2 1/2 ft.
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3.4yd.
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(figure available in print form)
TRAPEZOID
The area of a trapezoid is equal to the height times the average of the two parallel sides. Formula: A = h x(b + b2)
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____
2
(figure available in print form)
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1. Find the area of a trapezoid with bases of 44 inches and 36 inches and a height of 30 inches.
(figure available in print form)
A= 30x(44+36)
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44
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2
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+36
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Answer:1,200 sq.in.
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A= 30x40
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80
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A=1,200 sq.in.
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80-2=40
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Find the areas of trapezoids having the following dimensions.
heights
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8in
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5ft
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18ft.
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6ft.
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10in.
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upper base
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4in.
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9ft.
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29rd.
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11 3/4 ft.
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1ft.
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lower base
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10in.
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13ft.
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36rd.
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14 1/2 ft.
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1ft. 4in.
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DISCOVERING ¹
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1. Using a set of circles cut out of wood (circles approximately 8cm., 14cm., and 20cm. in diameter, for example) and a tape measure graduated in millimeters, measure the diameter and circumference of each. For each circle divide the circumference by the diameter.
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2. Draw circles 8cm., 14 cm., and 20cm., in diameter on a piece of graph paper ruled in millimeters. Determine the area of each circle by counting the number of square millimeters in each. For each circle divide the area (in square millimeters) by the square of the radius (in millimeters).
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3. Measure the diameter and volume of wooden spheres of three different diameters. This measurement can be made by immersing the spheres in water contained in graduated cylinders; the volume of water displaced is the volume of the spheres. For each sphere divide the volume by 4/3 times the radius cubed.
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4. The answer Obtained in each of these calculating should all be slightly greater than 3. If all of the measurements are made with a high degree of accuracy the answers would be very close to 22/7. This number appears frequently in studies of sciences and it is designated by the Greek symbol ¹. This number has been determined with great accuracy; to nine decimal places, for example, it is equal to 3.141592654. You have now learned the following:
(figure available in print form)
For a circle;
circumference = ¹ x (diameter)
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C = ¹ D
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area = ¹ x (radius squared)
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A = ¹ R
2
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For a sphere
volume = 4/3 ¹ x (radius cubed)
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V = 4/3 ¹ R
3
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For each of the following diameters calculated the circumference and area of a circle and the volume of a sphere: 25cm. (the diameter of a dinner plate); 66cm. (the diameter of a bicycle wheel); 8,000 feet (the diameter of the earth).
Sphere
The volume of a sphere is equal to 4/3 times pi (¹) times the cube of the radius. Formula V = 4/3 ¹ r
3
.
Sometimes the formula V= ¹d
3
is used.
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6
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1. Find the volumes of spheres having the following radii:
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a) 40 in
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b) 66ft
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c) 12.4 yd.
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d) 2 1/2 in.
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2. Find the volume of spheres having the following diameters:
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a) 25 ft.
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b) 74 in.
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c)10.2 ft.
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d) 8 1/2 in.
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VOLUME
The volume of a cube is equal to the length of the edge times itself times itself or the edge or side cubed. Formula: V = e
3
or V= s
3
.
1. Find the volume of a cube whose edge measures 17 inches.
(figure available in print form)
V=e3
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17
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289
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V=(17)
3
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x17
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x17
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V=17x17x17
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119
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2023
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V=4,913 cu.in.
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17
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289
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289
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4913
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Answer:4,913 cu.in.
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2. Find the volumes of cubes whose edges measure:
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a) 10ft.
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b) 15in.
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c) 11 1/2ft.
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d) 28ft.
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e) 1.08yd.
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f) 0.38 in.
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g)4 1/2ft.
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h) 5 3/4yd.
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i) 6yd.
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j) 7 1/2in.
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