Corey is trying to find the surface area of a tetrahedron. They sketch a net of the tetrahedron on their paper. The net shows four congruent, equilateral triangles, each with a base of 5 inches and a height of approximately 4.33 inches. What should Corey do next? Help Corey to find the surface area of the tetrahedron.(4 points)
To find the surface area of the tetrahedron, Corey needs to calculate the area of each of the four equilateral triangles and then add them together.
The formula for the area of an equilateral triangle is A = 1/2 * base * height.
Given that the base of each triangle is 5 inches and the height is approximately 4.33 inches, Corey should substitute these values into the formula to find the area of one triangle:
A = 1/2 * 5 * 4.33
A = 1/2 * 21.65
A = 10.825 square inches
Since there are four congruent triangles on the net, Corey should multiply the area of one triangle by 4 to get the total surface area of the tetrahedron:
Total surface area = 4 * 10.825
Total surface area = 43.3 square inches
Therefore, the surface area of the tetrahedron is 43.3 square inches.