Use the image to answer the question.
An illustration shows a hexagon with an inward triangle drawn from one of the sides. The triangle is marked A equals 4.
Find the area of the regular hexagon.
(1 point)
units
its 24😒
Use the image to answer the question.
An illustration shows a triangle with sides measuring 16 meters, 14 meters, and 8 meters. A dashed perpendicular line, from the side measuring 16 meters to the opposite angle, measures 7 meters. A right angle symbol is shown to the left of the perpendicular line.
A prism and pyramid have congruent triangular bases. If their heights are both 15 m, what is the volume of each shape?
(1 point)
The volume of the prism is ___ m3.
The volume of the pyramid is ___ m3.
We need to find the area of the base (triangular) first, using the given triangle measurements. Let's use Heron's formula to find the area:
s = (16 + 14 + 8)/2 = 19
area = √(s(s-16)(s-14)(s-8)) = √(19(3)(5)(11)) ≈ 52.3 m^2
Now, the volume of a prism is found by multiplying the area of the base by the height:
volume of prism = area of base x height = 52.3 x 15 = 784.5 m^3
The volume of a pyramid is found by multiplying the area of the base by the height and dividing by 3:
volume of pyramid = (area of base x height)/3 = (52.3 x 15)/3 = 261.5 m^3
Therefore, the volume of the prism is 784.5 m^3, and the volume of the pyramid is 261.5 m^3.
So the two answers are??
The volume of the prism is 784.5 m³ and the volume of the pyramid is 261.5 m³.
Ummm it says its wrong
I apologize for my mistake. I have rechecked my calculations and found that the volumes of the prism and the pyramid should be:
Volume of Prism = Base Area × Height = (1/2 × 8 × 7) × 15 = 420 cubic meters
Volume of Pyramid = (1/3) × Base Area × Height = (1/3 × 1/2 × 8 × 7) × 15 = 70 cubic meters
Therefore, the volume of the prism is 420 m³, and the volume of the pyramid is 70 m³.
Given a triangular pyramid and triangular prism with congruent bases and the same heights, what do you know about the relationship between the volume of each? Write your answer in fraction form.(1 point)
The volume of the pyramid is___ the size of the volume of the prism.
The volume of the pyramid is 1/3 times the size of the volume of the prism.
To find the area of a regular hexagon, we can use the formula:
Area = (3√3 * s^2) / 2
Where "s" is the length of one side of the hexagon.
Unfortunately, the image description does not provide the length of one side of the hexagon. It only mentions a triangle and its side length. Thus, we cannot directly determine the area of the regular hexagon using the given information.