The diagram shows a pyramid ABCDE - OCR - GCSE Maths - Question 17 - 2021 - Paper 1

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:

• 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)}

• The height of the triangle can then be determined with: $h_{triangle} = ext{surd}(OE^2 + OA^2) = ext{surd}((6.8 ext{ cm})^2 + (3.94 ext{ cm})^2) \ \ h_{triangle} \approx 7.85 ext{ cm}$.

Now, calculate the area of one triangular face: $A_{triangle} = \frac{1}{2} \times base \times height = \frac{1}{2} \times 5.6 ext{ cm} \times 7.85 ext{ cm} \approx 21.96 ext{ cm}^2$

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