Answer:
28
Step-by-step explanation:
Using a net to find the surface area of a rectangular prism
Finding the areas of each of the rectangles and squares of the net of a rectangular prism and adding up those areas gives the surface area or total surface area of the prism.
For example, if the length of one side of the cube 4 units then the area of one its face is 4 × 4 = 16 square units. From the net, we can see that there are six equal faces and so we get the total surface area is 6 × 16 = 96 square units.
Surface Area of a Rectangular Prism using Nets
A rectangular prism or cuboid is formed by folding a net as shown −
Cuboid
We can see from the net that there are two rectangles with dimensions 3 cm by 6 cm, two rectangles with dimensions 2 cm by 6 cm and two rectangles with dimensions 2 cm by 3 cm. The total surface area is then
2 × 3 × 6 + 2 × 2 × 6 + 2 × 2 × 3 = 72 cm2
Example 1:
Find the surface area of the given rectangular prism in square cm.
Rectangular Prism in Square cm
Solution
Step 1:
Using net, the surface area of a rectangular prism
= 2lw+wh+lh; l = 6 ; w = 5; h = 3
Step 2:
Surface area of given prism = 26×5+6×3+3×5
= 230+18+15
= 126 square cm
Example 2:
Find the surface area of the given rectangular prism in square cm.
Rectangular Prism Square cm
Solution
Step 1:
Using net, the surface area of a rectangular prism
= 2lw+wh+lh; l = 5; w = 6; h = 4
Step 2:
Surface area of given prism = 25×6+5×4+6×4
= 230+20+24
= 148 square cm
