Myths about teaching can hold you back
- Year 8
Finding a length in composite shapes
I can solve area problems of composite shapes involving whole and/or part circles where the area is known and the radius or diameter must be found.
- Year 8
Finding a length in composite shapes
I can solve area problems of composite shapes involving whole and/or part circles where the area is known and the radius or diameter must be found.
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Lesson details
Key learning points
- The diameter can be found from the area of circles or parts of circles by rearranging the formula.
- The radius can be found from the area of circles or parts of circles.
- The diameter or radius can be found from the area of composite shapes by reasoning and rearranging the formula.
Keywords
Sector - A sector is the region formed between two radii and their connecting arc.
Diameter - The diameter of a circle is any line segment that starts and ends on the edge of the circle and passes through the centre of the circle.
Radius - The radius is any line segment that joins the centre of a circle to its edge.
Common misconception
If I want to find the radius of a semicircle from its area, I halve the area first.
You must double the area. This calculates the area of a full circle, whose radius can be found by first dividing by π, then square rooting.
To help you plan your year 8 maths lesson on: Finding a length in 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: Finding a length in 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.
We use learning cycles to break down learning into key concepts or ideas linked to the learning outcome. Each learning cycle features explanations with checks for understanding and practice tasks with feedback. All of this is found in our slide decks, ready for you to download and edit. The practice tasks are also available as printable worksheets and some lessons have additional materials with extra material you might need for teaching the lesson.
The assessment exit quiz will test your pupils' understanding of the key learning points.
Our video is a tool for planning, showing how other teachers might teach the lesson, offering helpful tips, modelled explanations and inspiration for your own delivery in the classroom. Plus, you can set it as homework or revision for pupils and keep their learning on track by sharing an online pupil version of this lesson.
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.
Equipment
Licence
Prior knowledge starter quiz
6 Questions
Q1.Find the positive value of $$x$$ that is a solution to the equation: $$x^2 + 4 = 85$$. $$x=$$ .
Q2.Select the fully factorised form of this expression: $$42r + 56$$.
Q3.Find the positive value of $$x$$ that is a solution to the equation: $$3{\times}7{\times}2x^2 = 3{\times}56$$. $$x=$$
Q4.Select the fully factorised form of this expression: $$2kx^2 + 3kx$$.
Q5.A circle has a radius of 1.2 cm. Find the area of this circle. Give your answer in cm, rounded to 2 decimal places. Area = cm².
Q6.The area of a circle is 908 cm². Use the formula: $$area = {\pi} {\times}r^2$$ to form an equation and solve this equation to find the radius of the circle, rounded to the nearest integer. cm.
Assessment exit quiz
6 Questions
Q1.A quarter-circular sector is cut out of a circle. The quarter-circle has an area of 32$$\pi$$ cm². What was the area of the original circle?
Q2.A semi-circular sector is cut out of a circle. The semicircle has an area of 98$$\pi$$ cm². Which of these statements are true about the original circle?
Q3.This composite shape is composed of a quarter-circle and a square. The area of the composite shape is 114 cm². Which of these statements about the shape are correct?

Q4.This composite shape is composed of a quarter-circle and a square. The area of the composite shape is 216 cm². Which of these equations are correct steps in the method to find the radius?

Q5.The area of this composite shape is: ($$9216\pi + 16384$$) cm². Find the value of $$r$$. $$r=$$ .

Q6.This composite shape is composed of two quarter-circles and a square. The area of this composite shape is 1360 cm². Find the value of $$r$$, rounded to the nearest integer. $$r=$$
