Regular triangular pyramid has the slant height k=12 cm and lateral area AL = 198 cm2. Find the length of the base edge.
Accepted Solution
A:
To solve this we are going to use the formula for the lateral surface area of a regular pyramid: [tex]LSA= \frac{1}{2} pk[/tex] where [tex]LSA[/tex] is the lateral surface area. [tex]p[/tex] is the perimeter of the base. [tex]k[/tex] is the slant height.
We know for our problem that [tex]LSA=198[/tex] and [tex]k=12[/tex], so lets replace those values in our formula and solve for [tex]p[/tex]: [tex]LSA= \frac{1}{2} pk[/tex] [tex]198= \frac{1}{2} (p)(12)[/tex] [tex]198=6p[/tex] [tex]p= \frac{198}{6} [/tex] [tex]p=33[/tex]
Now we know that the perimeter of the base of our regular triangular pyramid is 33 cm. Remember that the perimeter of a triangle is the sum of its 3 sides. Since our pyramid is regular, its base will be an equilateral triangle, so to find the length of the base edge, we just need to divide the perimeter by 3: [tex]base.edge= \frac{33}{3} [/tex] [tex]base.edge=11[/tex]
We can conclude that the length of the base edge of our regular triangular pyramid is 11 cm.