Area of Triangles

Lesson 5.01

Lesson Objectives

After completing this lesson, you will be able to say: • I

can

use composition and decomposition to determine the area of triangles.

• I

can

compare the area of a triangle to the area of the composed rectangle.

• I

can

solve problems involving area of triangles.

Area

Area:

The amount of square units contained within a plane, or a two-dimensional figure.

Area of a Rectangle - Review

Count each square unit within the rectangle. There are 21 square units. This method works if you have the shape on a grid.

Area can be found with or without a coordinate plane by multiplying the length by the width.

7 × 3 = 21 square units.

Therefore, the area of this rectangle is 21 units squared.

How can you cut the rectangle to create 2 equivalent triangles?

We can create two equivalent triangles by cutting the rectangle across the diagonal.

By cutting the rectangle we have decomposed it.

Decomposition:

To separate a shape into smaller shapes.

Just like we can decompose the rectangle, we can also compose shapes as well. How can you use the triangles to compose a shape?

That’s right we can put shapes together to create a new shape.

Composition:

Putting shapes together to create another, larger shape.

Congruent

Congruent:

Having the exact same shape and measurements.

Area of a Triangle

Perpendicular Lines "Perpendicular" means two lines that intersect to form a right angle (90 degrees).

Calculating Area of a Triangle The formula for area of a triangle can be used to find the area of any type of triagle.

Area of an Acute Triangle

Area of an Right Triangle

Total Area

Can you cut this rectangle into 2 equivalent right triangles and one acute triangle?

Total Area

We can easily cut this rectangle into 2 equivalent right triangles and one acute triangle?

Total Area

You can find total area by deconstructing the rectangle into parts, finding the area of each part, then adding it up.

Total Area

• Using the same triangles from our earlier examples, use this example to see how you can find total area The area of the

acute triangle

was 24 square inches. The area of the

right triangle

was 12 square inches.

Area of all three triangles

= 24 + 12 + 12 = 48 square inches.

The area of the rectangle = 8 inches × 6 inches = 48 square inches.

Key Vocabulary

• Can you define these terms?

Area Decomposition Composition Congruent

Sum it Up!!!

Now that you completed this lesson, you should be able to say: I can use composition and decomposition to determine the area of triangles.

I can compare the area of a triangle to the area of the composed rectangle.

I can solve problems involving area of triangles.