8 (a) Work out the area of this trapezium. 6 cm ____________ / / / / 5 cm / / /___________/ 9 cm 4 cm (b) The circumference of a circle, in terms of $ u$, is 100 $ u$:cm. Work out the radius of the circle.

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8 (a) Work out the area of this trapezium - OCR - GCSE Maths - Question 8 - 2023 - Paper 3

Question 8

8 (a) Work out the area of this trapezium. 6 cm ____________ / / / / 5 cm / / /____... show full transcript

Step 1

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Answer

To find the area of the trapezium, we use the formula:

ext{Area} = rac{1}{2} imes (a + b) imes h

where $a$ and $b$ are the lengths of the parallel sides, and $h$ is the height between them. In this case, we have:

Substituting the values into the formula gives:

ext{Area} = rac{1}{2} imes (6 + 9) imes 4 = rac{1}{2} imes 15 imes 4 = 30 ext{ cm}^2

Thus, the area of the trapezium is 30 cm².

Step 2

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Answer

To find the radius of the circle, we start with the formula for the circumference, which is given as:

C = 2 imes rac{22}{7} imes r

where $C = 100 ext{ cm}$ . Setting up the equation:

100 = 2 imes rac{22}{7} imes r

This simplifies to:

100 = rac{44}{7} imes r

To isolate $r$ , we multiply both sides by $rac{7}{44}$ :

r = rac{100 imes 7}{44} = rac{700}{44} = rac{175}{11} ext{ cm} ext{ (approximately } 15.91 ext{ cm)}

Thus, the radius of the circle is approximately 15.91 cm.

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