PRE-ALGEBRA
Area: Triangles and Trapezoids
(10-2)
How do you
find the area
of a triangle?
If you divide a parallelogram in half using a diagonal line, the two halves are
congruent (equal) triangles.
Since a triangle is half of a parallelogram, the area of a triangle is half the area of a
parallelogram, or:
Area of a triangle = ½ (base · height)
The height (also known as altitude) of a triangle is the distance from the vertex
(corner) on top straight down to the base (bottom, or side the triangle is sitting on).
Example: Find the area of the following triangle.
A = ½bh
Use the formula for the area of a triangle.
=½·8·3
Replace the b with 8 and the h with 3.
A = 12
Simplify
2
PRE-ALGEBRA
Area: Triangles and Trapezoids
LESSON 10-2
Additional Examples
Find the area of the triangle.
A=
=
1
bh
2
Use the formula for area of a triangle.
1
• 13 • 6
2
Replace b with 13 and h with 6.
= 39
Simplify.
The area is 39 in.2.
PRE-ALGEBRA
Area: Triangles and Trapezoids
(10-2)
How do you To find the area of an irregular figure, break it up into regular shapes that you can find
find the area The areas of, like trapezoids, rectangles, and triangles.
of an
irregular (not Example: A builder needs to cover the side of the house shown in the picture with
siding (wood strips). How many square feet of siding does the builder need to do
regular)
this job?
figure
containing a
Area of the triangle
Area of the rectangle
triangle?
A = ½bh
A = bh
= ½ · 16 · 9
= 16 · 10
= 72
= 160
Add the two areas up to find the total area: 72 + 160 = 232
The builder needs 232 ft.2 of siding.
PRE-ALGEBRA
Area: Triangles and Trapezoids
LESSON 10-2
Additional Examples
Find the area of the figure.
Area of triangle
1
bh
2
1
=
• 45 • 20
2
A =
= 450
Area of rectangle
A = bh
= 45 • 30
= 1,350
Add to find the total: 450 + 1,350 = 1,800.
The area of the figure is 1,800 cm2.
PRE-ALGEBRA
Area: Triangles and Trapezoids
(10-2)
How do you A trapezoid is made up of two triangles (when divided by a diagonal line) that
find the area have the same heights (altitudes) but different bases.
of an
trapezoid?
Method 1: One way to find the area of a trapezoid is to trapezoid is to treat it like
an irregular figure and add up the areas of the two triangles that make it.
Example:
The area of the trapezoid is the sum of the areas of the two triangles that make
it: 18 + 12 = 30
The trapezoid is 30 cm.2
PRE-ALGEBRA
Area: Triangles and Trapezoids
(10-2)
Method 1: In a trapezoid, the bases are the parallel sides (b1 and b2) and the
height (h) is the same for both triangles.
Notice the area of the trapezoid is ½b1h + ½b2h. Using the Distributive Property,
b1h + ½b2h = ½h (b1 + b2), so the:
area of a trapezoid = ½h (b1 + b2)
PRE-ALGEBRA
Area: Triangles and Trapezoids
(10-2)
Example: The trapezoid below is a cross-section of the Erie Canal. Find the area of
the cross-section.
A = ½h (b1 + b2)
= ½ · 4 (28 + 40)
Use the formula for the area of a
trapezoid.
Replace h with 4, b1 with 28, and b2
with 40.
= ½ · 4 (68) Simplify
= 2 (68)
= 136
The area is 136 ft.2 (square ft.)
PRE-ALGEBRA
Area: Triangles and Trapezoids
LESSON 10-2
Additional Examples
Suppose that, through the years, a layer of silt and mud
settled in the bottom of the Erie Canal. Below is the resulting cross
section of the canal. Find the area of the trapezoidal cross section.
1
h(b1 + b2)
2
1
A =
• 3(31 + 40)
2
1
=
• 3(71)
2
1
=
• 213
2
A =
Use the formula for the area of a trapezoid.
Replace h with 3, b1 with 31, and b2 with 40.
Simplify.
= 106.5
The area of the cross section is 106.5 ft2.
PRE-ALGEBRA
Area: Triangles and Trapezoids
LESSON 10-2
Lesson Quiz
Find each area.
1. trapezoid PQRU
192 ft2
3. triangle QRS
28 ft2
2. triangle PTU
20 ft2
4. trapezoid PQSU
164 ft2
PRE-ALGEBRA