Formulae: Can I Use an Area Formula?

Use the following formulae to work out the areas of these shapes:

 

Rectangle

We must know:

• the base length
• the perpendicular height from the base to the top.

 

Area of rectangle = base × height

 

 

Parallelogram

We must know:

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

 

Area of parallelogram = base × height

 

 

Triangle

We 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 1

Can an area formula be used to work out the area of this parallelogram, and if so, which one?

 

 

Answer

This is a parallelogram.

We must know:

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

 

We know the base length and the slant height, but not the perpendicular height.

No, we cannot use the area formula.

 

 

Example 2

Can an area formula be used to work out the area of this triangle, and if so, which one?

 

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.

 

Yes, we can use the area formula:

Area of triangle = ½ base × height