# Grade Six Mathematics

## Answers to last week’s exercises

## Greetings, boys and girls.

I hope you had a great week at school. In our last session, we examined the concept of the area of a square and also, the area of a rectangle. This week, we’ll look at the concept of calculating the area of triangles and compound shapes.

Let’s begin.

## Area of a Triangle

The area of a triangle is the measure of the region enclosed within its three sides. It is typically calculated using the formula:

## Area of Triangle =

The base is the length of any one side of the triangle, and the height is the perpendicular distance from that base to the opposite vertex.

Let us now apply this formula to an example:

Example 1: Calculate the area of a triangle, with height 10cm and base 6cm.

Height= 10cm

Base= 6cm

Area of triangle =

Example 2:

Calculate the area of a triangle, with height 16cm and base 8cm.

Height= 16cm Base= 8cm

Area of triangle =

Review the examples above and complete the exercise below:

## Exercise 1

Complete the table below, by calculating the

Now boys and girls, if we’re given the area and base of a triangle and need to find the height, what’s the next step? Any ideas?

Let’s find out!

Calculating the height of a triangle given the area and base

To calculate the height of a triangle when given the area and base, we apply the following formula:

Height of Triangle =

Let us pay careful attention to the example below:

Example: 1

Calculate the height of a triangle, with an area of 16cm2 and a base of 4cm.

Height of triangle =

Let’s complete the table below:

## Exercise 2

Calculate the height of the following triangles:

Great job, pupils!

Let’s now examine another fun topic!

## Compound Shapes

Boys and girls, do you know what a compound shape is? Let’s find out.

A compound shape is any shape that is made up of two or more geometric shapes. They come in a variety of different forms.

Here are two examples of compound shapes:

## Examples of compound shapes

a. The shape below is made up of a square and a triangle. b. The shape below is made up of a square and a rectangle.

Let’s now take a look at the steps in calculating the area of a compound shape:

## Area of Compound Shapes

Last week, we covered the concept of area as the measure of space within a 2D shape, and how different shapes have specific formulas for calculating their areas. Therefore, when dealing with compound shapes, we can determine their total area by combining the appropriate formulas. (Review last week’s content).

A compound shape can be split into two or more smaller shapes and the area of these shapes can be found. The total area of the compound shape can be found by adding the smaller areas together.

Steps in calculating the area of a compound shape

In order to find the area of a compound shape:

1. Break down the compound shape into basic shapes.

2. Find the area of the basic shapes. 3. Add the areas.

Let us apply the steps listed above to an example:

Example 1

Find the area of the shape below: