Find the total surface area of this prism where the cross-section is an isosceles triangle.
13 cm
5 cm
10 cm
24 cm

The total surface area of the prism is 620 cm²

Step-by-step explanation:

The total area of the prism = lateral area + 2 (area of the cross-section)

The lateral area = perimeter of the cross-section × height

∵ The cross-section of the prism is an isosceles triangle

∵ The sides of the triangle are 13 cm, 13 cm, 24 cm

∵ The perimeter of the triangle is the sum of its sides

∴ The perimeter = 13 + 13 + 24 = 50 cm

∴ The perimeter of the cross-section = 50 cm

∵ The height of the prism is 10 cm

→ Use the rule of the lateral area above to find it

∴ The lateral area of the prism = 50 × 10 = 500 cm²

∵ The area of the triangle = × base × height

∵ The base of the triangle = 24 cm

∵ The height of the triangle = 5 cm

∴ The area of the triangle =   × 24 × 5 = 60 cm²

∴ The area of the cross-section = 60 cm²

→ Substitute the lateral area and the area of the cross-section in the rule

  of the total surface area above

∵ The surface area = 500 + 2(60)

∴ The surface area = 500 + 120

∴ The surface area = 620 cm²

∴ The total surface area of the prism is 620 cm²

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