Area of composite shapes
I can solve area problems of composite shapes involving whole and/or part circles.
Area of composite shapes
I can solve area problems of composite shapes involving whole and/or part circles.
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Lesson details
Key learning points
- The area parts of a circle can be found using the area formula and reasoning.
- The area of shapes made from circles and parts of circles can be found.
- The area of composite shapes that include circles can be found.
Keywords
Sector - A sector is the region formed between two radii and their connecting arc.
Common misconception
To find the area of a quarter-circle divide the radius by 4 to use as part of the calculation.
You must divide the area by 4, not the radius. The radius gets squared when calculating area so the division of r would be applied twice.
To help you plan your year 8 maths lesson on: Area of composite shapes, download all teaching resources for free and adapt to suit your pupils' needs...
To help you plan your year 8 maths lesson on: Area of composite shapes, download all teaching resources for free and adapt to suit your pupils' needs.
The starter quiz will activate and check your pupils' prior knowledge, with versions available both with and without answers in PDF format.
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The assessment exit quiz will test your pupils' understanding of the key learning points.
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Explore more key stage 3 maths lessons from the Perimeter, area and volume unit, dive into the full secondary maths curriculum, or learn more about lesson planning.
Licence
Prior knowledge starter quiz
6 Questions
Q1.What is $${2\over3}$$ of 144 cm?
Q2.Which of these formulae finds the area of a circle with radius $$r$$?
Q3.Find the area of a circle with radius of 25 cm, giving your answer both in terms of $$\pi$$ and in decimal form, rounded to 1 decimal place.
Q4.From its centre, this circle has been split up into 9 equally-sized sectors. How many degrees is the angle marked x?

Q5.Match each statement to the correct value for a circle with a diameter of 80 units.
The radius is -
40
The area in terms of $$\pi$$ -
1600$$\pi$$
The area in decimal form is -
5026.5
The circumference is -
80$$\pi$$
Q6.Which of these statements is true for this composite shape?

Assessment exit quiz
6 Questions
Q1.A quarter-circular sector is cut out of a circle. The original circle had an area of 120$$\pi$$ cm². What is the area of the quarter-circle?
Q2.A sector with a 60° angle is cut out of a circle. The original circle had an area of 3072 inches². The area of the sector is square inches.
Q3.Which of the following statements is true for this sector?

Q4.This composite shape is broken down into its component parts, made from circular sectors and quadrilaterals. Match each component part and composite shape to its area.

area of square -
4 cm²
area of semicircle -
$${1\over2}\pi$$ cm²
area of quarter-circle -
3.14 cm²
area of composite shape -
8.71 cm²
Q5.Which of these shows the area (written in terms of $$\pi$$) of the shaded region of this composite shape composed of a circular sector and a square?

Q6.What is the area (in cm²) of this composite shape, composed of only squares and circular sectors, rounded to the nearest integer? cm²
