AQA · Mathematics · 8300
GCSE Maths: Area: quarter-circle
Geometry & Measures · AQA GCSE Maths (8300). Cards are generated from the Corbettmaths practice questions and answers for Area: quarter-circle (Corbettmaths Video 47), and every card links back to the exact page it came from. Practice tests are drawn from this deck’s own cards. Source material © Corbettmaths — used with attribution.
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What is the formula for the area of a semicircle with radius r?
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½πr²
What is the formula for the area of a quarter-circle with radius r?
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¼πr²
If a semicircle has diameter d, what radius should be used in the area formula?
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r = d/2. The radius is half the diameter.
When calculating the area of a semicircular window in a rectangular wall, how do you find the paintable wall area?
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Multiply length × height for the rectangle, then subtract the semicircle area.
A goat tied to a fence with a rope traces what geometric shape as it moves?
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A semicircle (or portion of a circle), with the rope length as the radius.
What is a shaded segment in the context of a quarter-circle with a chord?
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The region between the arc and the chord. It equals the quarter-circle area minus the triangle area.
To find the radius of a semicircle given its area A, what formula should you use?
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r = √(2A/π). Rearrange A = ½πr² to solve for r.
In a composite field made of a triangle and a quarter-circle sharing a side, how do you find the total area?
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Calculate the triangle area and the quarter-circle area separately, then add them together.
What does 'leave your answer in terms of π' mean?
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Do not calculate π as a decimal (3.14159…). Leave π as the symbol in your final answer, e.g., 9π cm².
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