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The diagram shows two similar solid triangular prisms, A and B - Edexcel - GCSE Maths - Question 17 - 2022 - Paper 2

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The diagram shows two similar solid triangular prisms, A and B. The volume of prism A is 58.806 cm³ The volume of prism B is 1587.762 cm³ The cross section of each ... show full transcript

Worked Solution & Example Answer:The diagram shows two similar solid triangular prisms, A and B - Edexcel - GCSE Maths - Question 17 - 2022 - Paper 2

Step 1

The area of the triangle is 43.74 cm²

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Answer

To calculate the height of the triangle in prism A, we use the formula for the area of a triangle:

Area=12×base×heightArea = \frac{1}{2} \times base \times height

Given that the base (length of the base of the triangle) is 8.1 cm and the area of the triangle is 43.74 cm², we can rearrange the formula to solve for height (h):

43.74=12×8.1×h43.74 = \frac{1}{2} \times 8.1 \times h

Multiplying both sides by 2 gives:

87.48=8.1×h87.48 = 8.1 \times h

Now, divide both sides by 8.1 to find h:

h=87.488.110.80cmh = \frac{87.48}{8.1} \approx 10.80 \, cm

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