Answer:
S.A= 16x² + 30x + 6
S.A = 4πw² - 4π
S.A = 19y² + 14y
Explanation:
The figure is rectangular prism
∵ S.A = perimeter of base × height + 2 base area
∵ Perimeter of the base = 2(x + 3 + 2x + 1) = 2(3x + 4)
= 6x + 8
∵ Area of the base = (x + 3)(2x + 1) = 2x² + x + 6x + 3
= 2x² + 7x + 3
∴ S.A = (6x + 8)(2x) + 2(2x² + 7x + 3)
= 12x² + 16x + 4x² + 14x + 6
= 16x² + 30x + 6
The figure is cylinder
∵ S.A = perimeter of base × height + 2 base area
∵ Perimeter of the base = 2π(w - 1) = 2πw - 2π
∵ Area of the base = π(w - 1)² = π(w² - 2w + 1)
= πw² - 2πw + π
∴ S.A = (2πw - 2π)(w + 3) + 2(πw² - 2πw + π)
=2πw² + 6πw - 2πw - 6π + 2πw² - 4πw + 2π
= 4πw² - 4π
The figure is triangular prism
∵ S.A = perimeter of base × height + 2 base area
∵ Perimeter of the base = 2y + 2y + 1 + y + 3 = 5y + 4
∵ Area of the base = 1/2(2y)(2y + 1) =y(2y + 1)
= 2y² + y
∴ S.A = (5y + 4)(3y) + 2(2y² + y)
= 15y² + 12y + 4y² + 2y
= 19y² + 14y