Question

You buy a ring box as a birthday gift that is in the shape of a triangular prism. What is the least amount of wrapping paper needed to wrap the box?

(My picture is above.)

Answer 1

We are given triangular prism with height 8cm and three sides as 10 cm, 10.5 cm and 14.5 cm.

Now surface area is given by:

Area of three rectangular faces :

face 1: (l*w) = 8*10.5 = 84 cm²..................(1)

face 2: (l*w) = 8*10 = 80 cm² ....................(2)

face 3: (l*w) = 14.5 * 8 =116 cm² ..................(3)

Now we have two right angled triangles here with base 10 cm and height 10.5 cm.

Area of triangle is given by

`Area = (1)/(2) * base * height`

plugging base and height,

`Area = (1)/(2) * 10 * 10.5`

Area of two triangles = 105 cm²................(4)

Adding the four areas to get the total surface area

Area= 84 +116 +80 + 105 = 385 cm²

Answer : the least amount of wrapping paper needed to wrap the box is 385 square cm.