If all four dimensions of triangular prism having surface area as 288 is doubled than new surface area will be four times than the initial prism that is 1152 square unit.
Given that
Surface area of a triangular prism = 288 square unit
Need to evaluate new surface area if all four measurement of triangular prism is double.
Relation between surface area and the four dimensions of the triangular prism is given by following formula
Surface Area of triangular prism = bh + 2ls + lb
Where h is height of the prism , b is length of base of the prim , l is length of the prism and s is side length of the prism.
Given that Area of triangular prism = 288 square unit
=> bh + 2ls +lb = 288
Doubling the four dimensions means replace b by 2b, l by 2l , s by 2s and h by 2h in formula of Surface area of triangular prism.
[tex]\text { We get Surface area of new triangular prism }=2 b \times 2 h+2 \times 2 l \times 2 s+2 l \times 2 b[/tex]
[tex]\begin{array}{l}{=4 \times b h+4 \times 2 l s+4 \times l b} \\\\ {=4(b h+2 l s+l b)}\end{array}[/tex]
=> Surface area of new triangular prism = 4 (bh + 2ls +lb)
=> Surface area of new triangular prism = 4 x 288 = 1152 square unit.
Hence we can conclude that if all four dimensions of triangular prism having surface area as 288 is doubled than new surface area will be four times than the initial prism that is 1152 square unit.
Answer: C, the surface area increases by 4 times
Step-by-step explanation:
