GCSE OCR Maths Area: The diagram shows a pyramid ABCD

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 5.6cm. The vertex E is vertically above the centre O of the base. The he... show full transcript

Worked Solution & Example Answer:The diagram shows a pyramid ABCDE - OCR - GCSE Maths - Question 17 - 2021 - Paper 1

Step 1

Calculate the Area of the Base (ABCD)

96%

114 rated

Answer

The base ABCD is a square with side length 5.6 cm.

The area of the base can be calculated as:

ext{Area}_{ ext{base}} = ext{side}^2 = 5.6^2 = 31.36 ext{ cm}^2

Step 2

Calculate the Slant Height (ED)

99%

104 rated

Answer

To find the slant height ED, we can use the Pythagorean theorem in triangle OED.

We know that:

OE = 6.8 cm (height of the pyramid)
OD = \frac{5.6}{2} = 2.8 cm (half the length of the base)

Using the Pythagorean theorem:

ED = \sqrt{OE^2 + OD^2} = \sqrt{6.8^2 + 2.8^2}

Calculating those values:

= \sqrt{46.24 + 7.84} = \sqrt{54.08} \approx 7.35 ext{ cm}

Step 3

Calculate the Area of One Triangular Face (ABE)

96%

101 rated

Answer

The area of one triangular face (e.g., ABE) can be calculated using the formula:

ext{Area}_{ ext{triangle}} = \frac{1}{2} \times ext{base} \times ext{height}

The base AB = 5.6 cm and height (slant height) ED = 7.35 cm:

ext{Area}_{ ext{ABE}} = \frac{1}{2} \times 5.6 \times 7.35 \approx 20.52 ext{ cm}^2

Step 4

Calculate the Total Lateral Surface Area

98%

120 rated

Answer

Since there are 4 triangular faces, the total lateral surface area can be calculated as:

ext{Total_{lateral}} = 4 \times ext{Area}_{ ext{triangle}} \approx 4 \times 20.52 \approx 82.08 ext{ cm}^2

Step 5

Calculate the Total Surface Area of the Pyramid

97%

117 rated

Answer

Finally, the total surface area of the pyramid is the sum of the base area and the total lateral surface area:

ext{Total_{surface}} = ext{Area}_{ ext{base}} + ext{Total_{lateral}}

Substituting the values:

= 31.36 + 82.08 \approx 113.44 ext{ cm}^2

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

Worked Solution & Example Answer:The diagram shows a pyramid ABCDE - OCR - GCSE Maths - Question 17 - 2021 - Paper 1

Calculate the Area of the Base (ABCD)

Calculate the Slant Height (ED)

Calculate the Area of One Triangular Face (ABE)

Calculate the Total Lateral Surface Area

Calculate the Total Surface Area of the Pyramid

Join the GCSE students using SimpleStudy...

Other GCSE Maths topics to explore