Homework 1
Name: _____________________________________________ Chapter 10 Page 72 - 117
Practice 10.1 – Area of Triangles
Identify a base and a height of each triangle.
1)
2)
base: ________ height:________
base: ________ height:________
Label the base of each triangle with the letter b and the height with the letter h.
3)
5)
4)
6)
Homework 2
Find the area of each triangle.
7)
8)
The area of each triangle is 76 square inches.
Find the height. Round to the nearest tenth on an inch.
9)
10)
Homework 3
The area of each triangle is 45 square centimeters.
Find the base. Round to the nearest tenth of a centimeter if necessary.
11)
13)
12)
14)
Homework 4
Find the area of the shaded region.
15)
18)
(#17 Hint: use the rectangle, then subtract.)
16)
17)
19)
Homework 5
Use the graph to solve.
20) The coordinates of the vertices of a triangle are A(4, 7), B(4, 1) and C(8, 1). Find
the area of triangle ABC.
21) The coordinates of the vertices of a triangle are D(1, 7), E(-3, 2) and F(6, 2). Find
the area of triangle DEF.
22) The coordinates of the vertices of a triangle are J(-5, 2), K(1, -2) and L(5, -2). Find
the area of triangle JKL.
Homework 6
23) The area of triangle MNP is 17.5 square units. The coordinates of M are (-9, 5) and
the coordinates of N are (-2, 0). The height of triangle MNP is 5 units and is
perpendicular to the x-axis. Point P lies to the right of point N. Given that 𝑁𝑃 is the
base of the triangle, find the coordinates of point P.
24) The coordinates of the vertices of a triangle are X(1, 2), Y(-6, -2), and Z(1, -4). Find
the area of triangle XYZ. (Hint: Use the vertical side as the base.)
25) The coordinates of the vertices of a triangle are P(-2, 6), Q(-4, 2), and R(5, 1). Find
the area of triangle PQR. (Hint: Draw a rectangle around triangle PQR…then subtract)
Homework 7
Find the area of the shaded region.
26) Figure DGHJ is a trapezoid.
27) Figure ABCD is a rectangle. The length of
𝑍𝐵 is
28) The area of triangle PQS is
3
7
the length of 𝐴𝐵.
𝟕
of the area of trapezoid PRST. (Hint: I used the
𝟏𝟐
triangles and then a bar broken into 12 pieces.)
29) Figure EFHL is a parallelogram. The length of 𝐹𝐺 is
5
8
the length of ̅̅̅̅
𝐹𝐻.
Homework 8
Practice 10.2 – Area of Parallelograms and Trapezoids
Label a base and a height for each parallelogram. Use b and h.
1)
2)
3)
4)
Find the area of each parallelogram.
5)
6)
Homework 9
Label the bases and height for each trapezoid. Use 𝒃𝟏, 𝒃𝟐 , and h.
7)
8)
9)
10)
Find the area of each trapezoid.
11)
12)
Homework 10
The area of the parallelogram is 64 square inches. Find the height. Round your
answer to the nearest tenth of an inch.
13)
14)
The area of the trapezoid is 42 square centimeters. Find the height. Round your
answer to the nearest tenth of a centimeter.
15)
16)
Homework 11
17) The area of trapezoid ABCD is 503.25 square centimeters. Find the length of 𝑩𝑪.
18) The area of trapezoid EFGH is 273 square centimeters. Find the area of triangle
EGH.
19) The coordinates of the vertices of a parallelogram are P(0, 5), Q(-3, 0), R(2, 0), and
S(5, 5). Find the area of parallelogram PQRS.
Homework 12
20) Three out of the four coordinates of the vertices of parallelogram WXYZ are W(0, 1),
X(-4, -4) and Y(-1, -4). Find the coordinates of Z. Find the area of the parallelogram.
Point Z: ___________
21) The coordinates of the trapezoid EFGH are E(-3, 3), F(-3, 0), G(1, -4), and H(1, 4).
Find the area of the trapezoid.
Homework 13
22) Three out of four coordinates of the vertices of trapezoid ABCD are A(0, 1),B(-4, -4)
and C(-1, -4). 𝐴𝐷 is parallel to 𝐵𝐶. 𝐴𝐷 is 6 units. The point D lies to the right of point
A. Find the coordinates of point D. Then find the area of the trapezoid.
Point D: ___________
23) Parallelogram PQRT is made up of isosceles triangle PST and trapezoid PQRS.
Find the area of the parallelogram PQRT.
Homework 14
Practice 10.3 – Area of Other Polygons
Give the minimum number of identical triangles you could divide each regular
polygon into so that you could find the area of the polygon.
1)
2)
____________________
_______________________
Solve.
3) Derrick drew a regular pentagon with side lengths of 8 centimeters. He divided the
pentagon into 5 identical triangles, and measured the height of one of the triangles to be
5.5 centimeters. Find the area of the pentagon. (Figure not drawn to scale.)
Homework 15
4) Lydia drew a regular hexagon. She divided it into 6 identical triangles, and measured
the height of one of the triangles to be 4 inches. The area of the hexagon is 55.2
square inches. Find the length of each side of the hexagon.
Homework 16
Use the given information to find the area of each regular polygon.
6) The shaded area is 9.7 square in.
7) The shaded area is 12.8 square cm.
8) Suppose you have three identical equilateral triangles. Use a sketch to show how
you can make each of the following from two or more of the triangles. (use a ruler)
a) a quadrilateral whose area is two times as great as an equilateral triangle.
b) a quadrilateral whose area is three time as great as an equilateral triangle.
Homework 17
Each figure is made from a regular polygon surrounded by identical triangles.
Find the area of each figure.
9)
10)
Homework 18
Practice 10.4 – Area of Composite Figures
Draw straight lines to divide. Describe two was to find the area of each figure.
1) Divide the figure into a rectangle and two right triangles.
Area =
Area =
2) Divide the figure into a rectangle and two right triangles.
Area =
Area =
3) Divide the figure into a rectangle and a right triangle.
Area =
Area =
Homework 19
Draw straight lines to divide. Describe a way to find the area.
4)
5)
Area = ___________________________
_________________________________
Area = __________________________
Find the area of each figure.
6) Parallelogram ABDE is made up of square ACDF, triangle ABC, and triangle FDE.
Triangle ABC and triangle FDE are identical. The area of square ACDF is 36 square
meters. Find the area of triangle ABC. Then find the area of parallelogram ABDE.
Find the area of triangle EBC.
8) In the figure below, trapezoid ABDE is made up of three triangles, and figure ABCE is
a parallelogram. Find the area of triangle EBC if the area of trapezoid ABDE is 180
square centimeters.
Solve.
Homework 20
9) a) Plot the points P(-2, 2), Q(-2, -2), R(-4, -5), S(1, -5), and T(3, -2) on a coordinate
plane. Connect the points to form figure PQRST.
b) Find the area of figure PQRST.
c) Point V lies on 𝑄𝑇. The area of triangle PQV is
2
5
the area of triangle PQT. Plot point
V and give the coordinates of point V.
V: __________________
Find the area of trapezoid MNRS.
10) In the figure below, trapezoid MNRS is made up of trapezoid MNPT, triangle TPQ,
and parallelogram TQRS. The area of triangle TPQ is 84 square feet. The lengths of
𝑁𝑃, 𝑃𝑄, and 𝑄𝑅 are in the ratio 2: 1.5: 1. Find the area of trapezoid MNRS.
Homework 21
Find the area of triangle BDE.
11) The figure below is made up of two trapezoids ABEF and BCDE. The area of
triangle FGE is 26 square inches, and the area of trapezoid BCDE is 82.5 square
inches. BG is equal to GE. Find the area of BDE.
Find the area of the shaded region.
12)
3
8
of the triangle is shaded.
Homework 22
Find the height of trapezoid PQRS.
13) Trapezoid PQRS is made up of isosceles triangle PQS and triangle SQR. The area
of triangle PQS is 16.5 square inches. The areas of triangle PQS and triangle SQR are
in the ratio 2 : 3. Find the height of trapezoid PQRS.
Find the area of each figure.
14) In the figure below, trapezoid ABCD is made up of square BCDE and triangles ABF
and AFE. The area of square BCDE is 576 square feet. The ratio of BF to FE is 2 : 1.
Find the area of triangle ABF.
Homework 23
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