Answer:
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 = [tex]\frac{1}{2}[/tex] × base × height
∵ The base of the triangle = 24 cm
∵ The height of the triangle = 5 cm
∴ The area of the triangle = [tex]\frac{1}{2}[/tex] × 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
