1 thought on “The lateral surface rea of the right<br />triangular hyramid with the<br />length of the edge<br />3 en is. .”
Step-by-step explanation:
The first thing to realize is that a regular tetrahedron has 4 faces of equal area what are triangles. The area of one of these faces is 16(sqrt 3). The area of a triangle is (0.5)(base)(height). The base is the edge length we are looking for, we know the area so all we need to do is figure out the height.
However, we have been told that all the edges are the same so we know each face is an equilateral triangle with each interior angle equal to 60°. If you cut the face in half with with a line going from one vertice to the center of the opposite side you end up with a right triangle that has a hypotenuse equal to the edge length, a short side that is equal to 1/2 an edge length and a long side that is equal to the height of (1/2)(edge)(sqrt 3).
Putting this all into the original formula for the area of a face.
Area = (1/2)(edge)(height)
16(sqrt 3) = (1/2)(edge)[(1/2)(edge)(sqrt 3)]
Divide through by sqrt 3 and clean up the right side you have.
Step-by-step explanation:
The first thing to realize is that a regular tetrahedron has 4 faces of equal area what are triangles. The area of one of these faces is 16(sqrt 3). The area of a triangle is (0.5)(base)(height). The base is the edge length we are looking for, we know the area so all we need to do is figure out the height.
However, we have been told that all the edges are the same so we know each face is an equilateral triangle with each interior angle equal to 60°. If you cut the face in half with with a line going from one vertice to the center of the opposite side you end up with a right triangle that has a hypotenuse equal to the edge length, a short side that is equal to 1/2 an edge length and a long side that is equal to the height of (1/2)(edge)(sqrt 3).
Putting this all into the original formula for the area of a face.
Area = (1/2)(edge)(height)
16(sqrt 3) = (1/2)(edge)[(1/2)(edge)(sqrt 3)]
Divide through by sqrt 3 and clean up the right side you have.
16 = (1/4)(edge^2)
edge = 8 cm.