Answer:
paragraph proof
Step-by-step explanation:
Answer:
lateral surface area = 48 inches²
Step-by-step explanation:
The picture below is the square base pyramid you are referring. The lateral area is adding the area of the 4 triangles in the pyramid.
area of a triangle = 1/2 × b × h
The slant height of the triangle is gotten using Pythagoras theorem
lateral surface area = 4 × (1/2 × 3 × 8)
lateral surface area = 4 × 24/2
lateral surface area = 4 × 12
lateral surface area = 48 inches²
<span>Simplifying
3x + -1y = 12
Solving
3x + -1y = 12
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add 'y' to each side of the equation.
3x + -1y + y = 12 + y
Combine like terms: -1y + y = 0
3x + 0 = 12 + y
3x = 12 + y
Divide each side by '3'.
x = 4 + 0.3333333333y
Simplifying
x = 4 + 0.3333333333y</span>
Since the triangle is an equilateral triangle we know all of it's sides must be the same length, with that in mind the angles that make up the triangle must be equal as well. Knowing that a triangle's three interior angles make up 180 degrees we know that the size of each angle must be one third of this (as each angle must be equal).
180/3 = 60
then we may split the triangle along it's altitude into two special right triangles
more specifically two 30-60-90 triangles.
this means that the side with 30 degrees will be some value "x" where the side for 60 degrees will be related as it is "x*sqrt(3)" and the hypotenuse (which would be the side of the triangle) would be proportionally "2x"
this would mean that the altitude is the side associated with the 60 degree angle as such we can solve for "x" using this.
12= x*sqrt(3)
12/sqrt(3)=x
4sqrt(3)=x (simplifying the radical we get "x" equals 4 square root 3)
now we may solve for the side length of the triangle which is "2x"
2*4sqrt(3) -> 8sqrt (3)
eight square root of three is the answer.
