Answer:
Surface area = 228 square inches
Explanation:
We know that the surface area of a 3-dimensional shape is the same as the area of the 2-dimensional shapes.
If we were to make a net of this figure, we'd see that there are:
- 5 squares, whose sides each measure 6 inches,
- and 4 triangles, whose bases measure all measure 6 inches and whose heights all measure 4 inches
Step 1: We can find the area of one square and later multiply it by 5. The formula for area of a square is A = s^2, where
- A is the area in square units,
- and s is the side length
We can plug in 6 for s to solve for the area of one square:
A = 6^2
A = 36
Step 2: Now we can multiply this value by 5 to find the total area of the five squares that make up the figure:
Total area of squares = 5 * 36
Total area of squares = 180 square inches
Step 3: Similarly, we can find the area of one triangle and later multiply it by 4. The formula for area of a triangle is A = 1/2bh, where
- b is the base,
- and h is the height
We can plug in 6 for b and 4 for h to solve for the area of one triangle:
A = 1/2 * (6 *4)
A = 1/2 * 24
A = 12 square inches
Step 4: Now we can multiply this value by 4 to find the total area of the four triangles that make up the figure:
Total area of triangles = 4 * 12
Total area of triangles = 48 square inches
Step 5: Finally, we can add up the total area of the squares and the total area of the triangles to find the surface area of the composite figure:
SA = 180 + 48
SA = 228 square inches