Question
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)
Answers
GPT 3.5
To find the surface area of the tetrahedron, Corey should calculate the area of each of the four equilateral triangles in the net and then add them together.
The formula for the area of an equilateral triangle is:
Area = (1/2) x base x height
Given that the base of each triangle is 5 inches and the height is 4.33 inches, Corey can plug these values into the formula to find the area of one triangle:
Area = (1/2) x 5 x 4.33 = 10.83 square inches
Since there are four congruent triangles in the tetrahedron, Corey should multiply the area of one triangle by 4 to find the total surface area of the tetrahedron:
Total surface area = 4 x 10.83 = 43.32 square inches
Therefore, the surface area of the tetrahedron is 43.32 square inches.
The formula for the area of an equilateral triangle is:
Area = (1/2) x base x height
Given that the base of each triangle is 5 inches and the height is 4.33 inches, Corey can plug these values into the formula to find the area of one triangle:
Area = (1/2) x 5 x 4.33 = 10.83 square inches
Since there are four congruent triangles in the tetrahedron, Corey should multiply the area of one triangle by 4 to find the total surface area of the tetrahedron:
Total surface area = 4 x 10.83 = 43.32 square inches
Therefore, the surface area of the tetrahedron is 43.32 square inches.