Respuesta :
Answer:
72 + 36 square root 3
Step-by-step explanation:
equation for whole thing : LA + area of base
first need to find lateral area = sum of all lateral faces
to find 1 lateral face (1/2)(slant height)(side)
Given both (1/2)(6)(4) = 12
do times 6 = 12 times 6 = 72
that is your lateral area
Now need to fine area of hexagon
area of polygon = (1/2)( apothem)(perimeter)
perimeter = 4 times 6 = 24
For apothem need to find other sides of half triangle in midle which is a 30-60-90 triangle so short leg = 1/2 hypotenuse which given so 1/2 6 = 3
long leg = short times square root of 3 = 3 square root 3
that is apothom so (1/2)(3 square root 3)(24)= 36 square root 3
Put together to get 72 + 36 square root 3
The total area of the pyramid with side lengths of 4 and a slant height of 6 is gotten as; 24√3 + 72 square units
What is the are of the Pyramid?
We are given that the pyramid has a regular hexagonal base. Thus;
Side length of hexagonal base = Base of triangular face =4 units
Height of triangle =6 units
The total area of pyramid = A_b + A_l
Where;
A_b = Base area
A_l = Lateral area
Area of hexagonal base is given by the formula;
A = ³/₂(√3)a²
Where a = Side length
Thus, area of hexagonal base is;
A = ³/₂(√3)(4²)
A = 24√3 square units
Area of triangular face = ¹/₂ * 4 * 6 = 12 square units
In pyramid, there are 6 triangular faces. Thus, the lateral area of pyramid is;
Lateral Area = 6 * 12 = 72 square units
Thus;
Total Area of Pyramid = 24√3 + 72 square units
Read more about Pyramid Area at; https://brainly.com/question/5757743
