What is the surface area of the three-dimensional figure represented by this net?
The net pattern has a square base of side lengths 3 inches, 3 inches, 3 inches and 3 inches are attached with four congruent triangles of height 8 inches.
A.
57 square inches
B.
60 square inches
C.
105 square inches
D.
108 square inches
The surface area of a figure is the sum of the areas of all its faces.
In this case, the figure consists of a square base and four congruent triangles. The area of the square base is 3 inches x 3 inches = 9 square inches.
The area of each triangle can be calculated using the formula for the area of a triangle:
Area = (base x height) / 2
In this case, the base of each triangle is 3 inches and the height is 8 inches, so the area of each triangle is (3 inches x 8 inches) / 2 = 24 square inches.
Since there are four triangles, the total area of the triangles is 4 triangles x 24 square inches/triangle = 96 square inches.
Therefore, the total surface area of the figure is 9 square inches (base) + 96 square inches (triangles) = 105 square inches.
Therefore, the answer is C. 105 square inches.