Study Guide
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6.g.1—Find the area of triangles, quadrilaterals, and other polygons.
1.
Note: Figure is not drawn to scale.
If x = 14 units and h = 6 units, then what is the area of the triangle shown above?
A. 126 square units
B. 42 square units
C. 18 square units
D. 84 square units
2.
Note: Figure is not drawn to scale.
If x = 8 units, y = 3 units, and h = 2 units, then what is the area of the parallelogram shown
above?
A. 24 square units
B. 16 square units
C. 6 square units
D. 22 square units
3.
What is the area of the object above?
A. 34 cm2
B. 84 cm2
C. 14 cm2
D. 62 cm2
4. A toilet bowl cleaner has replaceable hexagonal heads. The diagram below shows the
replaceable head.
*Picture not drawn to scale
What is the area of the replaceable head? Round to the nearest hundredth, if necessary.
A. 15 square inches
B. 13.59 square inches
C. 12 square inches
D. 17.81 square inches
5.
Note: Figure is not drawn to scale.
If x = 13 units, y = 7 units, and h = 2 units, then what is the area of the trapezoid shown above?
A. 20 square units
B. 14 square units
C. 23 square units
D. 26 square units
6. Find the area of the regular pentagon below by using the area formula for triangles.
a = 6 inches and b = 8 inches
*picture not drawn to scale
A. 240 in
B. 15 in2
2
C. 120 in2
D. 48 in2
7. A baseball diamond is a square with corners at home plate, first base, second base, and third
base. The distance between home plate and first base is 30 yards. What is the area of a baseball
diamond?
A. 1,800 square yards
B. 90 square yards
C. 900 square yards
D. 120 square yards
8.
Note: Figure is not drawn to scale.
If x = 8 units and h = 6 units, then what is the area of the rhombus pictured above?
A. 10 square units
B. 48 square units
C. 16 square units
D. 32 square units
9.
11 units
9 units
What is the area of the rectangle above?
A. 20 square units
B. 108 square units
C. 99 square units
D. 40 square units
10.
11 units
What is the area of the square above?
A. 110 square units
B. 121 square units
C. 55 square units
D. 44 square units
Explanations
1. To find the area of the triangle, substitute the values given in the question into the formula
given below.
2. Use the formula for the area of a parallelogram.
Area = base • height
=x•h
= 8 units • 2 units
= 16 square units
3. Separate the object into 2 rectangles. There are several ways this could be done.
Consider the 12 cm by 4 cm rectangle on top of the object and the 7 cm by 2 cm rectangle on
bottom of the object.
Calculate the area of each rectangle by multiplying the length times the width.
12 cm × 4 cm = 48 cm2
7 cm × 2 cm = 14 cm2
Then, add the two areas together to get the total area of the object.
48 cm2 + 14 cm2 = 62 cm2
So, the object has an area of 62 cm2.
4. First, separate the hexagon into two triangles and a rectangle, as shown below.
Next, use the triangle and rectangle area formulas to find the areas of the two triangles and the
rectangle.
Then, add the areas of the two triangles and the rectangle to find the total area of the hexagon.
5. To find the area of the trapezoid, substitute the values given in the question into the formula
given below.
6. To find the area of the regular pentagon, divide the shape into triangles.
A regular pentagon has all congruent sides and all congruent angles.
Use the formula for the area of a triangle to find the area of the pentagon.
The formula for the area of a triangle is
× base × height.
Since there are five congruent triangles, multiply the area of one of the triangles by five to get
the total area of the five triangles that form the pentagon.
5 × ( × 8 in × 6 in) = 120 in2
So, the area of the pentagon is 120 in2.
7. A square is a type of rectangle. The area of a rectangle can be found using the formula below,
where l is the length of the rectangle, and w is the width of the rectangle.
A = lw
The length and width of a square are the same, so substitute l = 30 yards and w = 30 yards into
the area formula, and solve for A.
A = (30 yards)(30 yards)
= 900 square yards
8. To find the area, substitute the values given in the question into the formula given below.
Area = base • height
=x•h
= 8 units • 6 units
= 48 square units
9. To find the area of the rectangle, use the formula as shown below.
Area = length × width
= 9 units × 11 units
= 99 square units
10. The area of a square is given by the following formula.
Area = length × width
Since all four sides of a square are congruent, the length and width of the square are the same.
So, the area of the square can be found by squaring the given side length.
Area = (11 units)2
= 11 units × 11 units
= 121 square units