Answer:
a) 120 cm³
b) 184 cm²
Step-by-step explanation:
a) Please see the attached picture for reference.
[tex]\boxed{volume \: of \: prism = base \: area \times height}[/tex]
Volume of prism
= area highlighted in blue ×10cm
Let's find the base area (in blue).
[tex]\boxed{area \: of \: triangle = \frac{1}{2} \times base \times height}[/tex]
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.
[tex]\boxed{area \: of \: rectangle = length \times breadth}[/tex]
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
