How_To_Be_Good_At_Math

172 MEASUREMENT •^ AREAS OF TRIANGLES MEASUREMENT •^ AREAS OF PARALLELOGRAMS

Areas of triangles

Squares and rectangles aren’t the only shapes with a

handy formula to help us work out their area. We can also use

formulas to find the areas of other shapes, including triangles.

The area of any triangle is:

½ base × height

We can turn the triangle into a rectangle by

adding a second identical triangle. So, the

triangle takes up exactly half the rectangle's area.

We already know that the area of a rectangle

is: width × length. Here, the width of the

rectangle is equal to the base of the triangle, and

the length is equal to its height.

We also know the triangle has half the area

of the rectangle, so we can write a formula

for the area of a triangle like this:

Area of a triangle = ½ base x height

This scalene triangle looks a little trickier

to turn into a rectangle.

First, draw a straight line down from the top

vertex to the base to make it into two right-

angled triangles.

Now, it’s easy to turn these two triangles into

rectangles like we did before. This triangle takes

up half the area, too. So, the formula is the same:

Area of a triangle = ½ base x height

Look at this right-angled triangle. We're going

to use a formula to work out its area.

Make the

triangle into

a rectangle

BASE OF TRIANGLE

BASE

HEIGHT OF TRIANGLE HEIGHT

Right-angled triangles Other triangles

172_173_Areas_of_triangles_and_parallelograms.indd 172 29/02/2016 18:03