Question

Please help! I’m really struggling with this. It’s due in 1 hour.

Answer 1

a) 120 cm³

b) 184 cm²

Explanation:

a) Please see the attached picture for reference.

`\boxed{volume \: of \: prism = base \: area * height}`

Volume of prism

= area highlighted in blue ×10cm

Let's find the base area (in blue).

`\boxed{area \: of \: triangle = (1)/(2) * base * height}`

The base of the triangle is 10cm, and its height is 4cm.

Base area

= ½ ×6 ×4

= ½(24)

= 12 cm²

∴ volume of prism

= 12 ×10

= 120 cm³

b) Surface area of prism

= 2(area of blue triangle) +2(orange rectangle) +purple rectangle

Since the area of the blue triangle was found in part (a), let's find the area of the orange rectangle first.

`\boxed{area \: of \: rectangle = length * breadth}`

Area of orange rectangle

= 10 ×5

= 50 cm²

Area of purple rectangle

= 10 ×6

= 60 cm²

∴ surface area of prism

= 2(12) +2(50) +60

= 24 +100 +60

= 184 cm²