Question

Find the total surface area of these shapes

Answer 1

a) 420.1 m²

b)80.82 m²

Explanation:

1)a) Surface area of rectangular prism:

l = 12.5 cm ; w = 4 cm & h = 9.7 cm

`\boxed{\text{\bf Surface area of rectangular prism = 2*(lw +wh +hl)}}`

`\sf = 2* (12.5* 4 + 4*9.7 + 9.7*12.5)\\\\= 2* (50 + 38.8 + 121.25 )\\\\= 2* 210.05\\\\= 420.1 \ cm^2`

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b) Surface area of triangular prism:

base of triangle = b = 6 m

height of triangle = h = 8 cm = 0.08 m

`\sf s_1, s_2, s_3 \text{\sf are the sides of the triangle}\\\\s_1 = 6 \ m \ ; \ s_2 = 8 \ cm = 0.08 \ m ; s_3 = 10 \cm = 0.1 \ m`

length of the triangular prism = 13 m

`\boxed{\text{\bf Surface area of triangular prism = $\bf bh + (s_1+s_2+s_3)*l$)}}`

= 6*0.08 + (6 + 0.08 + 0.1)*13

= 0.48 + 6.18*13

= 0.48 + 80.34

= 80.82 m²