Answer:
6) LA = 90 units² and SA = 202 units²
7) LA = 377 units² and SA = 477.5 units²
8) LA = 208 units² and SA = 232 units²
9) LA = 455 units² and SA = 591 units²
Step-by-step explanation:
* Lets revise the rules of lateral area and surface area
- Lateral area of the solid = perimeter of its base × its height
- Surface area = lateral area + 2 × area of its base
* Now lets solve the problems
6) The solid is a rectangular prism
- Its base is a rectangle with dimensions 8 units and 7 units
- Its height is 3 units
∵ Perimeter of the rectangle = 2(L + W)
∴ Perimeter of the base = 2(8 + 7) = 2(15) = 30 units
∴ LA = 30 × 3 = 90 units²
∵ Area of the rectangle = L × W
∴ Area of the base = 8 × 7 = 56 units²
∴ SA = 90 + 2 × 56 = 90 + 112 = 202 units²
7) The solid is a cylinder
- Its base is a circle with diameter 8 units
∴ Its radius = 8 ÷ 2 = 4 units
- Its height is 15 units
∵ The perimeter of the circle is 2πr
∴ The perimeter of the base = 2π(4) = 8π
∴ LA = 8π(15) = 120π = 376.99 ≅ 377 units²
∵ The area of the circle = πr²
∴ The area of the base = π(4)² = 16π
∴ SA = 120π + 2 × 16π = 120π + 32π = 152π = 477.5 units²
6) The solid is a triangular prism
- Its base is a triangle with sides 5 , 5 , 6 units and height 4 units
- Its height is 13 units
∵ Perimeter of the triangle is the sum of the 3 sides
∴ Perimeter of the base = 5 + 5 + 6 = 16 units
∴ LA = 16 × 13 = 208 units²
∵ Area of the triangle = 1/2 × base × height
∴ Area of the base = 1/2 × 6 × 4 = 12 units²
∴ SA = 208 + 2 × 12 = 208 + 24 = 232 units²
9) The solid is a prism
- Its base is an isosceles trapezium with parallel bases 7 units and 10
units, 2 non-parallel bases 9 units and height 8 units
- Its height is 13 units
∵ Perimeter of the trapezium is the sum of its sides
∴ Perimeter of the base = 7 + 10 + 9 + 9 = 35 units
∴ LA = 35 × 13 = 455 units²
∵ Area of the trapezium = 1/2(b1 + b2) × h
∴ Area of the base = 1/2(7 + 10) × 8 = 68 units²
∴ SA = 455 + 2 × 68 = 455 + 136 = 591 units²
and 
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