A triangular pyramid has a base shaped like an equilateral triangle. The legs of the equilateral triangle are all 5 inches long, and the height of the equilateral triangle is 4.3 inches. The pyramid's slant height is 5 inches. What is its surface area?
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A triangular pyramid has a base shaped like an equilateral triangle. The legs of the equilateral triangle are all 13 meters long, and the height of the equilateral triangle is 11.3 meters. The pyramid's slant height is 20 meters. What is its surface area?
Why did the triangular pyramid go to a math tutor? Because it wanted to "shape" up its surface area skills! Let's get down to business and solve this together:
To find the surface area of the triangular pyramid, we need to calculate the area of the base and the area of the three identical triangular faces.
The area of an equilateral triangle can be found using the formula: (side length^2 * √3) / 4.
In this case, the side length of the equilateral triangle is 5 inches, so the area of the base is:
(5^2 * √3) / 4 = (25 * √3) / 4 = (25√3) / 4
Now, let's calculate the area of one triangular face. We know the slant height is 5 inches, and the height of the equilateral triangle is 4.3 inches.
The formula to find the area of a triangle is: (base * height) / 2.
Since the base of the triangle is also 5 inches, the area of one triangular face is:
(5 * 4.3) / 2 = 21.5 / 2 = 10.75
Since there are three identical triangular faces, the total area of all three faces is:
3 * 10.75 = 32.25
To find the surface area, we add the area of the base and the total area of the triangular faces:
(25√3) / 4 + 32.25 = (25√3) / 4 + 32.25
And there you have it! I hope that didn't "tri-angle" your brain too much. The surface area of the triangular pyramid is [(25√3) / 4] + 32.25 square inches.
To find the surface area of the triangular pyramid, we need to find the areas of all its faces and then sum them up.
First, let's begin by calculating the area of the equilateral triangle base. The formula to find the area of an equilateral triangle is:
Area = (side length^2 * √3) / 4
Since the side length of the equilateral triangle is given as 5 inches, we can substitute this value into the formula:
Area of base = (5^2 * √3) / 4
Area of base = (25 * √3) / 4
Next, let's calculate the areas of the triangular faces. We have four triangular faces in total.
The formula to calculate the area of a triangle given its base and height is:
Area = (base * height) / 2
For each face, the base is 5 inches (the slant height), and the height is 4.3 inches. Therefore, the area of each triangular face is:
Area of each face = (5 * 4.3) / 2
Now, let's calculate the total surface area by summing up the area of the base and the areas of the four triangular faces:
Surface area = Area of base + 4 * Area of each face
Finally, we can substitute the values we calculated to find the surface area of the triangular pyramid:
Surface area = (25 * √3) / 4 + 4 * [(5 * 4.3) / 2]
Simplify the equation further to find the numerical value of the surface area.
Impatient much?
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anyway....
It sound like your pyramid is a tetrahedron, that is, it is made from 4 equilateral triangles
So the surface area would simply be 4 times the area of an equilateral triangle with sides 5
Area of one of them = (1/2)(5)(4.3)
= ...
Now multiply that by 4