### Key Concepts

• Solving constant speed problems.

• Solving unit price problems.

• Using an equation to represent unit rate problems.

- Classification of triangles by angles

- Find the area of the triangle:

Count squares in the triangle:

Full squares =12

Half squares =8 means =4 squares

Area of the triangle =12 full squares + 8 half squares

=12 +4

=16 Square units

- When the perpendicular distance between a pair of lines is the same throughout, it can be called parallel lines

The **altitude of a triangle** is the perpendicular line segment drawn from the vertex to the opposite side of the triangle.

**Example 1:**

A parallelogram can be decomposed into two identical triangles. How you use the formula of area of parallelogram to find the area of triangle?

- Identical triangles have the same base and height, so they also have the same area

Area of triangle =12 area of parallellogram

Area of triangle A=1/2 .bh Sq.units

The area of one triangle is **half** the area of the related parallelogram.

- Area of parallelogram A=bh Sq.units
- Area of Triangle A= 1/2 of the area of parallelogram Sq.units

Th area of triangle = 1/2 b.h Sq.units

- Two identical triangles from a parallelogram with a base of 8 inches and height of 6 inches. What is the area of each triangle? Explain.

A diagonal divides the parallelogram into two identical triangles with same base and height then the area of triangles are equal.

Given that

Base of the triangle = 8 in

Height of the triangle=6 in

Area of the triangle = ½ bh Sq.units

= 1/2 x 8 x 6

=4 x 6

= 24

Area of each triangle is 24in2

**Example 2:**

A = ½ bh

A = ½ x 8 x8

= 32

∴

The area of the side of the birdhouse is 32 square inches

Example 3:

Kaylan drew the triangle shown below. What is the area of triangle?

Any side of a triangle can be its base. The height is the perpendicular distance from the base to the height of the opposite vertex

One way

A = ½ bh

A= ½ 10 x 8

A= 40

The area is 40 square feet.

Another way

A = ½ bh

A= ½ 16 x 5

A= 40

The area is 40 square feet.

**Key concept: **

- Find the area of triangle

**Solution:**

Given that,

height(h)= 2 ft

base(b)= 4 ft

Area of the triangle = 1/2xbh

= 1/2 x 4 x 2

= 4 square feet

- Find the area of triangle

**Solution:**

Given that,

height(h)=3.5 in

base(b)=4.2 in

Area of the triangle = ½bh

= ½ x 4.2 x 3.5

=7.35 square inches

- find the area of triangle

**Solution: **

Given that,

Height= 6.5 cm

base = 5 cm

Area of the triangle = ½ bh

= ½ x 5 x 6.5

= 2.5 x 6.5

= 16.25

Area of the triangle is 16.25 square centimeters.

Practice and problem solving:

- The base of the triangle is 2ft. The height of the triangle is 15 in. find the area of the triangle in square inches?

Given that,

Height = 15 in

base = 2ft

= 2 x 12 (∵1ft=12 in)

= 24 in

Area of the triangle = ½ bh

= ½ 24 x 15

= 12 x 15

= 180

Area of the triangle is 16.25 square centimeters.

- The dimensions of the sail for Erica’s sail boat are shown. Find the area of the sail?

Given that ,

the dimensions of the sail are

height = 15ft

base = 9ft

Area of the sail = ½ bh

= ½ 9 x 15

= 9 x 7.5

= 67.5

∴ *Area of the sail is 67.5* ft^{2}

## Exercise:

1. The vertices of a triangle are A (0,0),B (3, 8) and C (9, 0). What is the area of this triangle?

2. If you know the area and the height of the triangle, how can you find the base?

3. Find the height and the base where the base is twice the height and the area is 49 ne

4. Find the area of the triangle if the base and height are 20 cm, 2 m respectively?

5. What is the formula for base when the height and area is given?

6. Find the area of the triangle where the base is 10 cm and the height is 20 cm?

7. Find the area of triangle with the base 25 cm and the height 25 cm?

8. Find the base of the triangle where the area is 2 cm2 and the height is 2 cm?

### What have we learned?

• Solving constant speed problems.

• Solving unit price problems.

• Using an equation to represent unit rate problems.

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