Perimeter and area with money
Sometimes perimeter and area questions can be combined with other sections of the course such as managing money. In this case you will also have to work out a cost.
Question
A garden is in the shape of a rectangle measuring \(18.6\,m\) by \(11.8\,m\).
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.
Each packet holds \(600\,g\) of seed and costs \(\pounds6.19\).
How much will the gardener pay to buy enough packets to do this job?
As in a previous example we calculate the area of one triangle.
The area of the triangle \(=54.87\,m^{2}\)
Weight of seed recommended \(=54.87\,\times\,30 = 1646.1\,g\)
Each packet has \(600\,g\) of seed so the gardener needs 3 packets.
Cost \(=3\,\times\,6.19\,=\pounds18.57 \)
Question
The window at the top of the door is in the shape of a semicircle.
The door is \(1.2\,m\) wide.
The glass in the window is broken and needs to be replaced.
The replacement glass costs \(\pounds15.60\) per square metre plus a cutting and fitting fee of \(\pounds53\).
How much will it cost to repair the glass?
As in a previous example we calculate the area of the semicircle.
Area of circle \( =\pi r^{2}\)
\(=3.14\,\times0.6\,\times0.6\)
\(=1.1304\,m^{2}\)
Area of semicircle \(=\,0.57\,m^{2}\,\,(to\,\,2\,\,decimal\,\,places)\)
Cost of glass \(=0.57\,\times\,15.60=\pounds8.89\)
Cost of repair \(=8.89\,+53=\pounds61.89\)