Perimeter and area
Calculate the perimeter and area of triangles, quadrilaterals, composite shapes and sectors using appropriate formulas.
Worked examples
Area of a trapezium
Straightforward
Problem
A driveway is shaped like a trapezium with parallel sides of m and m and a perpendicular height of m. Find the area of the driveway.
1
Write the formula for the area of a trapezium.
2
Identify the values: m, m, m.
, ,
3
Substitute the values and evaluate.
m²
Answer
m²
Area of a composite shape
Moderate
Problem
The end section of a running track consists of a rectangle m long and m wide joined to a semicircle of diameter m. Find the total area of this shape, to 2 decimal places.
1
Find the area of the rectangle.
m²
2
Find the radius of the semicircle.
m
3
Find the area of the semicircle using .
m²
4
Add the two areas to find the total.
m²
Answer
m²
Arc length and sector area
Challenging
Problem
A sector of a circle has a radius of cm and a central angle of . Find (a) the arc length and (b) the area of the sector. Give answers to 2 decimal places.
1
Write the formula for arc length and substitute the values.
2
Evaluate the arc length to 2 decimal places.
cm
3
Write the formula for the area of a sector and substitute the values.
4
Evaluate the sector area to 2 decimal places.
cm²
Answer
(a) cm (b) cm²
Practise
Q1·Straightforward
A rectangular courtyard has a length of m and a width of m. Calculate the perimeter of the courtyard.
Explanation
m
Q2·Straightforward
A rectangular paddock has a length of m and a width of m. Calculate the area of the paddock.
Explanation
m²
Q3·Straightforward
A triangle has a base of cm and a perpendicular height of cm. Calculate the area of the triangle.
Explanation
cm²
Q4·Straightforward
A trapezium has parallel sides of m and m, and a perpendicular height of m. Calculate the area of the trapezium.
Explanation
m²
Q5·Moderate
A garden is shaped like a rectangle m long and m wide, with a right-angled triangular corner removed. The removed triangle has legs of m and m. Find the area of the garden.
Explanation
Area of rectangle m². Area of triangle m². Area of garden m².
Q6·Moderate
An isosceles triangle has a base of cm. Each of the two equal sides is cm long. Find the area of the triangle.
Explanation
The height bisects the base, giving a right triangle with base cm and hypotenuse cm. cm. Area cm².
Q7·Moderate
A shape is made by joining a rectangle m wide and m tall with a triangle on top. The triangle has a base of m and a perpendicular height of m. Find the total area of the shape.
Explanation
Area of rectangle m². Area of triangle m². Total area m².
Q8·Moderate
A rectangular piece of cardboard is cm wide and cm tall. A semicircle with diameter cm is cut from the bottom edge. Find the remaining area, to 2 decimal places.
Explanation
Radius cm. Area of rectangle cm². Area of semicircle cm². Remaining area cm².
Q9·Challenging
A sector of a circle has a radius of cm and a central angle of . Find the area of the sector. Give your answer to 2 decimal places.
Explanation
cm².
Q10·Challenging
A sector of a circle has a radius of m and a central angle of . Find the arc length of the sector. Give your answer to 2 decimal places.
Explanation
m.
Q11·Challenging
A block of land is divided into two parts: a rectangle m long and m wide, and a triangle with a base of m and a perpendicular height of m. Find the total area of the land.
Explanation
Area of rectangle m². Area of triangle m². Total area m².
Q12·Challenging
A shape consists of a rectangle m long and m wide, with a quarter circle of radius m attached to one of the shorter ends. Find the total area of the shape. Give your answer to 2 decimal places.
Explanation
Area of rectangle m². Area of quarter circle m². Total area m².