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Over Chapter 10 A. A B. B C. C D. D 160
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Over Chapter 10
A. A
B. B
C. C
D. D
(x + 3)2 + (y – 2)2 = 9
Write an equation of the circle with center at (–3, 2) and a diameter of 6.
Over Chapter 10
A. A
B. B
C. C
D. D
A. chord
B. diameter
C. secant
D. tangent
Which of the following figures is always perpendicular to a radius of a circle at their intersection on the circle?
• Find perimeters and areas of parallelograms.
• Find perimeters and areas of triangles.
Perimeter and Area of a Parallelogram
Find the perimeter and area of
Perimeter Since opposite sides of a parallelogram are congruent, RS UT and RU ST. So UT = 32 in. and ST = 20 in.
Perimeter and Area of a Parallelogram
Area Find the height of the parallelogram. The height forms a right triangle with points S and T with base 12 in. and hypotenuse 20 in.
c2 = a2 + b2 Pythagorean Theorem
202 = 122 + b2 c = 20 and a = 12
400 = 144 + b2 Simplify.
Perimeter = RS + ST + UT + RU
= 32 + 20 + 32 + 20
= 104 in.
Perimeter and Area of a Parallelogram
256 = b2 Subtract 144 from each side.
16 = b Take the positive square root of each side.
A = bh Area of parallelogram
= (32)(16) or 512 in2 b = 32 and h = 16
The height is 16 in. UT is the base, which measures 32 in.
Answer: The perimeter is 104 in. and the area is 512 in2.
A. A
B. B
C. C
D. D
88 m; 405 m2
A. Find the perimeter and area of
Area of a Parallelogram
Step 1 Use a 45°-45°-90° triangle to find theheight h of the parallelogram.
Find the area of
Area of a Parallelogram
Recall that if the measure of the legopposite the 45° angle is h, then themeasure of the hypotenuse is
Substitute 9 for themeasure of the
hypotenuse.Divide each side by .
≈ 6.36 Simplify.
Area of a Parallelogram
Step 2 Find the area.
A = bh Area of a parallelogram
≈ (12)(6.36) b = 12 and h = 6.36
≈ 76.3 Multiply.
Answer: 76.3 square units
Perimeter and Area of a Triangle
SANDBOX You need to buy enough boards to make the frame of the triangular sandbox shown and enough sand to fill it. If one board is 3 feet long and one bag of sand fills 9 square feet of the sandbox, how many boards and bags do you need to buy?
Perimeter and Area of a Triangle
Step 1 Find the perimeter of the sandbox.
Perimeter = 16 + 12 + 7.5 or 35.5 ft
Step 2 Find the area of the sandbox.
Area of a triangle
b = 12 and h = 9
Perimeter and Area of a Triangle
Step 3 Use unit analysis to determine how many ofeach item are needed.
Boards
Bags of Sand
boards
Perimeter and Area of a Triangle
Answer: You will need 12 boards and 6 bags of sand.
Round the number of boards up so there is enough wood.
A. A
B. B
C. C
D. D
12 boards and 14 bags of mulch
PLAYGROUND You need to buy enough boards to make the frame of the triangular playground shown here and enough mulch to fill it. If one board is 4 feet long and one bag of mulch covers 7 square feet, how many boards and bags do you need to buy?
Use Area to Find Missing Measures
ALGEBRA The height of a triangle is 7 inches more than its base. The area of the triangle is 60 square inches. Find the base and height.
Step 1 Write an expression to represent eachmeasure.
Let b represent the base of the triangle.Then the height is b + 7.
Step 2 Use the formula for the area of a triangle tofind b.
Area of a triangle
Use Area to Find Missing Measures
Substitution
120 = (b)(b + 7) Multiply each side
by 2.
120 = b2 + 7b DistributiveProperty
0 = b2 + 7b – 120 Subtract 120 from
each side.
0 = (b – 8)(b + 15) Factor.
b – 8 = 0 and b + 15 = 0 Zero ProductProperty
b = 8 b = –15 Solve for b.
Use Area to Find Missing Measures
Step 3 Use the expressions from Step 1 to findeach measure.
Since a length cannot be negative, the basemeasures 8 inches and the heightmeasures 8 + 7 or 15 inches.
Answer: b = 8 in., h = 15 in.
A. A
B. B
C. C
D. D
base = 28 in. and height = 40 in.
ALGEBRA The height of a triangle is 12 inches more than its base. The area of the triangle is 560 square inches. Find the base and the height.
