140580/04/SP/25©Cambridge University P ress & A ssessment 202219 The cross-section of a prism is an equilateral triangle of side 6 cm.The length of the prism is 20 cm.Calculate the total surface area of the prism.
Question
140580/04/SP/25©Cambridge University P ress & A ssessment 202219 The cross-section of a prism is an equilateral triangle of side 6 cm.The length of the prism is 20 cm.Calculate the total surface area of the prism.
Solution
To calculate the total surface area of the prism, we need to find the area of the triangular faces and the rectangular faces.
Step 1: Calculate the area of the equilateral triangle The formula for the area of an equilateral triangle is (sqrt(3)/4) * side^2. So, the area of one triangular face is (sqrt(3)/4) * 6^2 = 9sqrt(3) cm^2.
Since there are two triangular faces, the total area of the triangular faces is 2 * 9sqrt(3) = 18sqrt(3) cm^2.
Step 2: Calculate the area of the rectangular faces The rectangle sides are the same length as the triangle sides and the prism length, so each rectangle is 6 cm by 20 cm. The area of one rectangle is 6 * 20 = 120 cm^2.
Since there are three rectangular faces, the total area of the rectangular faces is 3 * 120 = 360 cm^2.
Step 3: Add the areas together The total surface area of the prism is the sum of the areas of the triangular and rectangular faces, which is 18sqrt(3) + 360 cm^2.
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