10.8.4 Self-Check on Areas

Tick iconExercise 7: Area of Grass

Now the gardener wants to calculate the area of turf that will be needed to grass the remainder of the unfenced section of garden, which includes the pond, as shown in the diagram below.

Using the values from Exercises 4 and 6 calculate the are of turf needed in m2 to the nearest m2.

Solutions icon

Answer

Area of a rectangle equals length multiplication width

So comma area of unfenced garden including pond equals left parenthesis 40 m en dash 10 m right parenthesis multiplication 20 m

prefix of equals 600 m squared

Area of circle equals pi multiplication left parenthesis radius right parenthesis squared

Diameter of pond equals two m

Radius equals diameter solidus two

So radius equals two m solidus two

prefix of equals one m

So area of pond equals pi multiplication left parenthesis one m right parenthesis squared

prefix of equals 3.142 m squared times left parenthesis to three d full stop p full stop right parenthesis

Total area of turf equals 600 m squared times en dash 3.142 m squared

prefix of equals 597 m squared times left parenthesis to the nearest one m squared right parenthesis

Hence the area of turf required is 597 m2.

Tick iconExercise 8: Area of Central Park, New York

Central Park in New York has an area of 3.41 km2. Convert this into m2.

Solutions icon

Answer

Since one km equals 1000 m

one km squared times prefix of equals 1000 m multiplication 1000 m

prefix of equals 1,000,000 m squared

So area of Central Park equals 3.41 multiplication 1,000,000 m squared

prefix of equals 3,410,000 m squared

Hence the area of Central Park in New York is 3,410,000 m2.

10.8.3 Self-Check on Perimeters

10.8.5 Self-Check on Volumes