Perimeter and area

Most perimeter and area questions at National 5 are set in problem situations.

Example

A garden is in the shape of a rectangle measuring \(16.3m\) by \(12.4m\).

The gardener marks out the two diagonals and decides to sow grass seeds on one of the four triangles formed by the intersection.

The seed packet states that \(30\,g\) of seed are recommended per square metre.

What weight of seed will he need?

Answer

Making a rough sketch of the shape is usually helpful (not a scale drawing).

You may choose any of the triangles as they are all the same area in a rectangle.

The area of the shaded triangle can be worked out as either \( \frac{1}{4}\,\,\times16.3\,\times\,12.4 = 50.53\,m^{2} \) (based on dividing the area of the rectangle by four) or \( \frac{1}{2}\,\,\times16.3\,\times\,6.2 = 50.53\,m^{2} \) (based on \(\frac{1}{2} \times base \times height\) where the height is half of \(12.4m\)).

Weight of seed recommended \( =50.53\,\times 30 = 1515.9\,g\)