Example 3: Calculating the area of a trapezoid using a formula
Calculate the area of the
wading pool.
Solution
A 5 (a 1 b) 3 h 4 2
5 (3 m 1 5 m) 3 3 m 4 2
58m33m42
5 24 m2 4 2
5 12 m2
This is the formula for the area of a trapezoid, where a and
b represent the lengths of the parallel sides. You can choose
these values: a = 3 m, b = 5 m, and h = 3 m. (You could have
chosen a = 5 m and b = 3 m instead.)
Substitute these values into the formula.
The area of the wading pool is 12 m2.
Checking
4.
Draw the following trapezoid on grid paper.
Calculate the area of the trapezoid by
dividing the shape into simpler shapes.
6.
Calculate the area of this trapezoid using
a formula.
Practising
5.
164
7.
a) Which side length of the trapezoid below
is not required to calculate its area?
b) Calculate the area and the perimeter of
the trapezoid to the nearest tenth.
8.
On centimetre grid paper, draw a trapezoid
with an area of 13 cm2.
Trace trapezoid ABCD, and show how two
trapezoids form a parallelogram. Calculate
the area of trapezoid ABCD.
Chapter 5
NEL
9.
Calculate the area of each trapezoid.
a)
b)
10.
11.
NEL
A garden has the dimensions shown below.
Which calculation could you use to find the
area of the garden? Explain your thinking.
a) Area 5 (3 m 1 1 m) 3 4 m 4 2
b) Area 5 1 m 1 (4 m 3 3 m) 4 2
c) Area 5 (4 m 1 1 m) 3 3 m 4 2
d) Area 5 (1 m 1 3 m) 3 4 m 4 2
e) Area 5 (4 m 1 3 m) 3 1 m 4 2
A trapezoid has an area of 10.5 cm2 and
parallel sides that measure 5.0 cm and
2.0 cm. What is the height of the trapezoid?
Explain what you did.
12.
a) A trapezoid has parallel sides that are
28 cm and 40 cm long, and 18 cm
apart. Calculate the area of the
trapezoid.
b) Another trapezoid has parallel sides
that are 2 m and 5 m long, and 3 cm
apart. Calculate its area.
13.
A trapezoid has an area of 20 cm2 and a
height of 5 cm. What is the sum of its top
and bottom sides?
14
. A kindergarten classroom has 10 trapezoidshaped tables. Some Grade 7 students have
volunteered to paint game boards to cover
the top surfaces of the tables. Each table
has the measurements shown. What is the
total area the students will paint?
Extending
15.
Use what you know about trapezoids to
calculate the area of this regular hexagon.
Explain what you did.
16.
The length of the shortest side of a red
pattern block is 25 mm. What is the area of
the trapezoid?
2-D Measurement
165