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The diagram shows a shape ABCDE - OCR - GCSE Maths - Question 7 - 2019 - Paper 4

Question 7

The diagram shows a shape ABCDE. The shape is made from a rectangle, a right-angled triangle and a quarter of a circle. F is the mid-point of BD. AE = 18m and... show full transcript

Worked Solution & Example Answer:The diagram shows a shape ABCDE - OCR - GCSE Maths - Question 7 - 2019 - Paper 4

Step 1

First, calculate the radius of the quarter circle

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Answer

Given that the length of AE is 18 m, this is also the length of the radius for the quarter circle. Thus, the radius (r) is 9 m.

Step 2

Now, find the lengths of each side of the shape

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Answer

The rectangle ABED has a length of 18 m and a height of 41 m. The right triangle FCD has a base equal to half of BD, thus BF = 18/2 = 9 m. The remaining height from F to C is then calculated using the Pythagorean theorem:

$ext{BC} = ext{hypotenuse} = \sqrt{(9^2 + 41^2)} = \sqrt{81 + 1681} = \sqrt{1762} \approx 41.93 m$

Step 3

Perimeter Calculation

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Answer

The perimeter P of shape ABCDE is given by: $P = AB + BC + CD + DE + EA + radius$
Substituting the lengths: $P = 18 + 41.93 + 18 + 41 + 9 = 127.93 m$ . Thus, rounding gives the perimeter as approximately 128 m.

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