PRE-ALGEBRA

PRE-ALGEBRA

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.

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).

Since a triangle is half of a parallelogram, the area of a triangle is half the area of a parallelogram, or:

Example: Find the area of the following triangle.

A = ½bh Use the formula for the area of a triangle.

A = 12 SimplifyThe area is 12 cm.2 (square cm.)

= ½ · 8 · 3 Replace the b with 8 and the h with 3.

Area: Triangles and Trapezoids (10-2)

PRE-ALGEBRA

Find the area of the triangle.

The area is 39 in.2.

A = bh Use the formula for area of a triangle.12

= • 13 • 6 Replace b with 13 and h with 6.12

= 39 Simplify.

Area: Triangles and TrapezoidsLESSON 10-2

Additional Examples

PRE-ALGEBRA

How do you find the area of an irregular (not regular) figure containing a triangle?

To find the area of an irregular figure, break it up into regular shapes that you can findThe areas of, like trapezoids, rectangles, and triangles.

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 this job?

Area of the triangle Area of the rectangleA = 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.

Area: Triangles and Trapezoids (10-2)

PRE-ALGEBRA

Find the area of the figure.

Add to find the total: 450 + 1,350 = 1,800.

12

The area of the figure is 1,800 cm2.

Area: Triangles and TrapezoidsLESSON 10-2

Additional Examples

Area of triangle Area of rectangle

A = bh12

A = bh

= • 45 • 20

= 450

= 45 • 30

= 1,350

PRE-ALGEBRA

How do you find the area of an trapezoid?

A trapezoid is made up of two triangles (when divided by a diagonal line) that have the same heights (altitudes) but different bases.

Example:

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.

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

Area: Triangles and Trapezoids (10-2)

PRE-ALGEBRA

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)

Method 1: In a trapezoid, the bases are the parallel sides (b1 and b2) and the

height (h) is the same for both triangles.

Area: Triangles and Trapezoids (10-2)

PRE-ALGEBRA

Example:

A = ½h (b1 + b2) Use the formula for the area of a

trapezoid. = ½ · 4 (28 + 40) 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.)

The trapezoid below is a cross-section of the Erie Canal. Find the area of the cross-section.

Area: Triangles and Trapezoids (10-2)

PRE-ALGEBRA

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.

The area of the cross section is 106.5 ft2.

A = h(b1 + b2) Use the formula for the area of a trapezoid.12

A = • 3(31 + 40) Replace h with 3, b1 with 31, and b2 with 40.12

= • 3(71) Simplify.12

= • 21312

= 106.5

Area: Triangles and TrapezoidsLESSON 10-2

Additional Examples

PRE-ALGEBRA

Find each area.

1. trapezoid PQRU 2. triangle PTU

3. triangle QRS 4. trapezoid PQSU

28 ft2

192 ft2 20 ft2

164 ft2

Area: Triangles and TrapezoidsLESSON 10-2

Lesson Quiz