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 the p... show full transcript
Worked Solution & Example Answer:The diagram shows a shape ABCDE - OCR - GCSE Maths - Question 7 - 2019 - Paper 4
Step 1
Step 1: Calculate the radius of the quarter circle
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Answer
The radius of the quarter circle is equal to the length AE, which is 18 m.
Step 2
Step 2: Determine the length BD
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Answer
Since F is the midpoint of BD, then BD is twice the distance from B to F. The perpendicular distance from C to AE is given as 41 m, which adds to the length AE to give the total height BD = 41 m.
Step 3
Step 3: Find the lengths of sides AB and DE
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Answer
The length of AB is equal to AE, which we determined as 18 m. The length DE is equal to the line segment from D to E, which we do not need to calculate as it's part of the rectangle.
Step 4
Step 4: Calculate the perimeter of the shape ABCDE
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Answer
The perimeter is calculated using the formula:
Perimeter = AB + BC + CD + DE + EA.
Here, AB = 18 m, BC = 41 m, CD = 18 m (as derived from the shape's dimensions), DE = radius of the quarter circle = 9 m (from the calculation of radius, since the diameter is of length 18 m).
Thus, the total perimeter is:
Perimeter = 18 + 41 + 18 + 9 = 86 m.
