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The diagram shows a pyramid ABCDE - OCR - GCSE Maths - Question 17 - 2021 - Paper 1
Question 17
The diagram shows a pyramid ABCDE. The pyramid has a square horizontal base ABCD with side 5.6 cm. The vertex E is vertically above the centre O of the base. The h... show full transcript
Worked Solution & Example Answer:The diagram shows a pyramid ABCDE - OCR - GCSE Maths - Question 17 - 2021 - Paper 1
Step 1
Step 2
Calculate the Area of Triangular Faces
Answer
Each triangular face (e.g., triangle ABE) has a base equal to the side of the square base and a height that can be calculated using the Pythagorean theorem.
The height of each triangle can be found as follows:
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The length from the center O to a vertex (e.g., A) is half the diagonal of the square base: d = rac{ ext{side} imes ext{surd}(2)}{2} = rac{5.6 ext{ cm} imes ext{1.414}}{2} \ ext{(approximately 3.94 cm)}
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The height of the triangle can then be determined with: .
Now, calculate the area of one triangular face:
Step 3
Total Surface Area of the Pyramid
Answer
Since there are 4 triangular faces: A_{total aces} = 4 \times A_{triangle} \approx 4 \times 21.96 ext{ cm}^2 = 87.84 ext{ cm}^2
Finally, the total surface area is: ext{Surface Area} = A_{base} + A_{total aces} \approx 31.36 ext{ cm}^2 + 87.84 ext{ cm}^2 \approx 119.20 ext{ cm}^2