To find the lateral surface area of the triangular pyramid, we need to find the area of each triangular face and then add them together.
Since the base is an equilateral triangle, all three sides are of equal length. Let's say each side has a length of s.
Given the net representation, there are three triangular faces on the sides of the pyramid. These triangular faces are also equilateral triangles with side lengths equal to s.
The formula for the area of an equilateral triangle is: Area = (sqrt(3) / 4) * side^2
Therefore, the area of each triangular face is: Area = (sqrt(3) / 4) * s^2
Now, we need to find the total lateral surface area by adding the areas of the three triangular faces:
Total lateral surface area = 3 * (sqrt(3) / 4) * s^2
= 3(sqrt(3) / 4) * s^2
= (3sqrt(3) / 4) * s^2
So, the lateral surface area of the triangular pyramid with an equilateral base represented in the net is (3sqrt(3) / 4) * s^2.
Find the lateral surface area of the triangular pyramid with an equilateral base represented in the net. (1 point)
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what the fart
I apologize for the confusion in my previous response. Let me correct that.
Given the net representation of the triangular pyramid with an equilateral base, we can see that there are three identical triangular faces forming the sides of the pyramid.
Each of these triangular faces is an equilateral triangle with side length, let's say, s. To find the lateral surface area, we need to find the area of one triangular face and then multiply it by the number of faces.
The formula for the lateral surface area of a triangular pyramid is:
Lateral Surface Area = (1/2) * perimeter of base * slant height
Since the base is an equilateral triangle, the perimeter is 3 times the length of one side:
Perimeter of base = 3s
The slant height is the height of one of the triangular faces. If we examine the net representation, we can see that the height of the pyramid is the height of one of the triangular faces. It forms a right triangle with the slant height being the hypotenuse and half of the base length (s/2) being one of the legs. To find the slant height (h), we can use the Pythagorean theorem:
h^2 = (s/2)^2 + h^2
h^2 = (s^2/4) + h^2
h = sqrt(3/4) * s
Now, we can substitute the values into the formula for lateral surface area:
Lateral Surface Area = (1/2) * 3s * sqrt(3/4) * s
= (3/2) * s^2 * sqrt(3/4)
= (3/2) * s^2 * sqrt(3)/2
= (3sqrt(3)/4) * s^2
Therefore, the lateral surface area of the triangular pyramid with an equilateral base represented in the net is (3sqrt(3)/4) * s^2.
Given the net representation of the triangular pyramid with an equilateral base, we can see that there are three identical triangular faces forming the sides of the pyramid.
Each of these triangular faces is an equilateral triangle with side length, let's say, s. To find the lateral surface area, we need to find the area of one triangular face and then multiply it by the number of faces.
The formula for the lateral surface area of a triangular pyramid is:
Lateral Surface Area = (1/2) * perimeter of base * slant height
Since the base is an equilateral triangle, the perimeter is 3 times the length of one side:
Perimeter of base = 3s
The slant height is the height of one of the triangular faces. If we examine the net representation, we can see that the height of the pyramid is the height of one of the triangular faces. It forms a right triangle with the slant height being the hypotenuse and half of the base length (s/2) being one of the legs. To find the slant height (h), we can use the Pythagorean theorem:
h^2 = (s/2)^2 + h^2
h^2 = (s^2/4) + h^2
h = sqrt(3/4) * s
Now, we can substitute the values into the formula for lateral surface area:
Lateral Surface Area = (1/2) * 3s * sqrt(3/4) * s
= (3/2) * s^2 * sqrt(3/4)
= (3/2) * s^2 * sqrt(3)/2
= (3sqrt(3)/4) * s^2
Therefore, the lateral surface area of the triangular pyramid with an equilateral base represented in the net is (3sqrt(3)/4) * s^2.
1 answer