Lesson
8
Surface Area of Prisms
Learning Intent: Calculate SA using nets and formulas.
Rectangular Prism
Total area of all 6 rectangular faces.
$$TSA = 2(lw + lh + wh)$$
Triangular Prism
Total of 2 triangular ends + 3 rectangular sides.
$$TSA = (2 \times Area_{Tri}) + Area_{Rects}$$
QUIZ Test Yourself
- Calculate the TSA of a cube with side length $4\text{m}$.
- A box has dimensions $l=10, w=5, h=2$. Find its Total Surface Area.
Show Answers
1. $6 \times (4^2) = 6 \times 16 = 96\text{m}^2$
2. $2(50 + 20 + 10) = 2(80) = 160\text{units}^2$
Practice Problem 8.1
A rectangular shipping crate is $3\text{m}$ long, $2\text{m}$ wide, and $1.5\text{m}$ high. Calculate the total surface area to be painted.
Step 1: $lw = 3 \times 2 = 6$
Step 2: $lh = 3 \times 1.5 = 4.5$
Step 3: $wh = 2 \times 1.5 = 3$
Total: $2(6 + 4.5 + 3) = 27\text{m}^2$