The surface area of the triangular prism is 1950 square inches, computed by summing the areas of its constituent triangles and rectangles.
Surface area refers to the measure of the total area that the surface of an object occupies. It is a crucial geometric concept that varies for different shapes and dimensions in geometry, encompassing diverse forms like spheres, cubes, cuboids, cones, and cylinders. Each geometric shape possesses unique formulas for calculating its surface area.
Considering the provided net for a triangular prism with side lengths a, b, and c, and altitude d, the surface area is computed by summing the areas of its constituent shapes – two triangles and three rectangles. The formula for the total surface area is given as:
Total Surface Area = Surface Area of Triangle + Surface Area of Rectangle
Detailed calculations involve substituting the given values for side lengths and altitude into the formulas for the surface area of a triangle and a rectangle. For the triangular prism described, the total surface area is determined as:
Total Surface Area = d * a + b * a + 2 * c * b
Substituting the given values (d = 20, a = 44, b = 14, and c = 30), the calculation yields:
Total Surface Area = (22 * 45) + (12 * 45) + 2 * (30 * 14) = 1950
Therefore, the surface area of the given figure is 1950 square inches.