The surface area of the pyramid is superfluous to calculating the slant height as the slant height is the height of the triangular side of the pyramid which can be worked out using Pythagoras on the side lengths of the equilateral triangle:
side² = height² + (½side)²
→ height² = side² - ¼side²
→ height² = (1 - ¼)side²
→ height² = ¾side²
→ height = (√3)/2 side
→ slant height = (√3)/2 × 9cm = 4.5 × √3 cm ≈ 7.8 cm.
However, the surface area can be used as a check:
140.4 cm² ÷ (½ × 9 cm × 7.8 cm) = 140.4 cm² ÷ 35.1 cm² = 4
So the pyramid comprises 4 equilateral triangles - one for the base and 3 for the sides; it is a tetrahedron.
Area = 0.5*base*perpendicular height
To find the height of the triangles on the sides of the pyramid, we use pythagorean theorem. We slice vertically through the center of the pyramid to find a triangle with base of 6.3 and height of 4. Using the pythagorean theorem, we can find that each side of this triangle will be sqrt(42+3.152). This will be the height of the triangles on the sides of the pyramid, let's call it h.So, the area of each triangle will be 1/2*6.3*h. There are 4 of these triangles.The area of the base of the pyramid will be 6.32The total surface area of the pyramid will be SA = 2*6.3*sqrt(42+3.152)+6.32SA ~= 103.84 m2
Cube, equilateral pyramid, and sphere.
It is impossible to answer the question without knowing the shape of the base, which will determine how many sloped triangles there are.
Area of a triangle = (base x height)/2 If the pyramid is made up of four identical triangles then it's surface area will be 2 x base x height. Remeber the height is the distance from the base of a triagle to the oposite point.
Volume: If it's a square-based pyramid then its just "the base times the height, divided by 3" or in short b2h/3 where b is one side of the base. and h is height. Surface area: 2bs+b2 where s is the perpendicular height from the bottom of any one of the triangles, to the top of the tip.
In effect an equilateral triangle is made up of two right angle triangles joined together so use Pythagoras' theorem to find the height:- 182-92 = 243 and the square root of this will be the height of the equilateral triangle which is about 15.588 cm
Cutting the equilateral triangle in half results in two right triangles each with a base of length x/2, and angles of 30, 60, and 90 degrees. Using the lengths of sides of a 30-60-90 triangle it can be found that the height is (x/2)√(3), which is the same as the height of the equilateral triangle.So the height of the equilateral triangle is x√(3) / 2.
A pyramid is a generic term used to describe a polyhedron with a polygonal base and triangles rising from that base to meet at an apex. The polygonal base can have any number, n, of sides, provided that n>2. There is, therefore, no information about the number of lateral faces in the pyramid. Also, the surface area of a pyramid depends on its height and there is no information whatsoever about its height. It is, therefore, impossible to answer such an underspecified question.
the base is a 2-d square with joined triangles, meeting together to make a corner at the top, the triangles height can be any height, or the square can be any size
Using Pythagoras' theorem it is impossible for an equilateral triangle with equal sides of 10 inches to have a height of 7 inches.