You should already know the following formula to work out the area of a **rectangle**:

You must know:

- the
**base**length - the perpendicular
**height**from the base to the top.

Area of **rectangle** = base × height

Now, try this with a piece of paper.

Start with a rectangle.

Cut off a right-angled triangle from the left-hand side and separate the two pieces.

The area of the two pieces together will be the same as the original rectangle.

Cut off a right-angled triangle from the right-hand side to form a triangle in the middle, and separate the three pieces.

The area of the three pieces will still be the same as the original rectangle.

Now look carefully at the pieces marked A and B below.

Notice that the areas match.

A matches A and B matches B.

So the **area of the triangle** in the middle is **half the area of the rectangle**.

**Area of Triangles**

You must know:

- the
**base**length - the perpendicular
**height**from the base to the apex.*(NOT the slant heights)*

Area of **triangle** = ½ base × height

or

Area of **triangle** = base × height ÷ 2

**Example**

Calculate the area of this triangle in cm^{2}.

**Answer**

This is a triangle.

We must know:

- the
**base**length - the perpendicular
**height**from the base to the top.*(NOT the slant height)*

If we turn our heads to the left, the **base length is 12 cm **and the **perpendicular height** **is** **6 cm**.

*We do not need to know the slant height of 10 cm to use the formula.*

Now we use the area formula:

**Area of triangle = ½ base × height**

**Area** = ½ × 12 × 6 = 6 × 6 = **36 cm ^{2}**

Or...

**Area of triangle = base × height ÷ 2**

**Area** = 12 × 6 ÷ 2 = 72 ÷ 2 = **36 cm ^{2}**