Five-Minute Check (over Chapter 10)
CCSS
Then/Now
New Vocabulary
Postulate 11.1: Area Addition Postulate
Key Concept: Area of a Parallelogram
Example 1: Perimeter and Area of a Parallelogram
Example 2: Area of a Parallelogram
Postulate 11.2: Area Congruence Postulate
Key Concept: Area of a Triangle
Example 3: Real-World Example: Perimeter and Area of a Triangle
Example 4: Use Area to Find Missing Measures
Over Chapter 10
Name a radius.
A.
B.
C.
D.
Over Chapter 10
Name a chord.
A.
B.
C.
D.
Over Chapter 10
Name a diameter.
A.
B.
C.
D.
Over Chapter 10
A. 90
B. 120
C. 160
D. 170
Over Chapter 10
Write an equation of the circle with center at
(–3, 2) and a diameter of 6.
A. (x + 3) + (y – 2) = 9
B. (x – 3) + (y + 2) = 6
C. (x + 3)2 + (y – 2)2 = 9
D. (x – 3)2 + (y + 2)2 = 6
Over Chapter 10
Which of the following figures is always
perpendicular to a radius of a circle at their
intersection on the circle?
A. chord
B. diameter
C. secant
D. tangent
Content Standards
G.GPE.7 Use coordinates to compute
perimeters of polygons and areas of triangles
and rectangles, e.g., using the distance
formula.
Mathematical Practices
1 Make sense of problems and persevere in
solving them.
7 Look for and make use of structure.
You found areas of rectangles and squares.
• Find perimeters and areas of parallelograms.
• Find perimeters and areas of triangles.
• base of a parallelogram
• height of a parallelogram
• base of a triangle
• height of a triangle
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
Perimeter = RS + ST + UT + RU
= 32 + 20 + 32 + 20
Area
= 104 in.
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 and Area of a Parallelogram
256 = b2
Subtract 144 from each
side.
16 = b
Take the positive square
root of each side.
The height is 16 in. UT is the base, which measures
32 in.
A = bh
= (32)(16) or 512 in2
Area of parallelogram
b = 32 and h = 16
Answer: The perimeter is 104 in. and the area is
512 in2.
A. Find the perimeter and area of
A. 88 m; 255 m2
B. 88 m; 405 m2
C. 88 m; 459 m2
D. 96 m; 459 m2
Area of a Parallelogram
Find the area of
Step 1
Use a 45°-45°-90° triangle to find the
height h of the parallelogram.
Area of a Parallelogram
Recall that if the measure of the leg
opposite the 45° angle is h, then the
measure of the hypotenuse is
Substitute 9 for the
measure 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
Find the area of
A. 156 cm2
B. 135.76 cm2
C. 192 cm2
D. 271.53 cm2
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 of
each item are needed.
Boards
boards
Bags of Sand
Perimeter and Area of a Triangle
Round the number of boards up so there is enough
wood.
Answer:
You will need 12 boards and 6 bags of sand.
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?
A. 12 boards and
14 bags of mulch
B. 11 boards and
13 bags of mulch
C. 12 boards and
13 bags of mulch
D. 11 boards and
14 bags of mulch
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 each
measure.
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 to
find b.
Area of a triangle
Use Area to Find Missing Measures
Substitution
120 = (b)(b + 7)
120 = b2 + 7b
0 = b2 + 7b – 120
0 = (b – 8)(b + 15)
b – 8 = 0 and b + 15 = 0
b=8
b = –15
Multiply each side
by 2.
Distributive
Property
Subtract 120 from
each side.
Factor.
Zero Product
Property
Solve for b.
Use Area to Find Missing Measures
Step 3
Use the expressions from Step 1 to find
each measure.
Since a length cannot be negative, the base
measures 8 inches and the height
measures 8 + 7 or 15 inches.
Answer: b = 8 in., h = 15 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.
A. base = 56 in. and height = 10 in.
B. base = 28 in. and height = 40 in.
C. base = 20 in. and height = 56 in.
D. base = 26 in. and height = 38 in.