hi clara95
Welcome to the forum.
Your triangle method and answer are correct. I'm not quite sure what you're doing for the trapezoid method. The usual formula for the area of a trapezoid is sum of the parallels divide by 2 and multiply by the distance between them. The parallels are 16 and 8; the distance between is the same as the apothem you have already worked out so the calculation becomes
(16+8)/2 x 4√3 x 2 as there are two such trapezoids.
Hope that helps,
Bob
Problems like the ones listed here require a picture for a better, deeper, fuller grasp. Agree?
]]>Welcome to the forum.
Your triangle method and answer are correct. I'm not quite sure what you're doing for the trapezoid method. The usual formula for the area of a trapezoid is sum of the parallels divide by 2 and multiply by the distance between them. The parallels are 16 and 8; the distance between is the same as the apothem you have already worked out so the calculation becomes
(16+8)/2 x 4√3 x 2 as there are two such trapezoids.
Hope that helps,
Bob
]]>I've been having problems with a particular exercise about finding the area of a Hexagon being divided into two trapezoids, each side measuring 8 cm. Step 1 was to find the area of a hexagon using the triangle method which was quite easy. This is the exercise:
1. Find the area of a regular hexagon with 8 feet sides. Round the answers to the nearest whole number. (2 pts.)
Part 1: Show your work using the triangle method taught in Lesson 21.
Part 2: Find the area of the same hexagon using two trapezoids. Confirm that the answers to Part 1 and Part 2 are equivalent.
Part 3: Construct a prism from the above regular hexagon. The height of the hexagonal prism is 5 feet. Find the surface area and the volume of this prism.
First, I drew a diagram
Forming 6 congruent triangles
draw the height or apothem of one of the triangles
each central angle is 360/6=60°
the apothem forms two 30-60-90 right triangles
the side opposite the 30° angle is half the hypotenuse
you have a right triangle with an 8-foot hypotenuse and one leg being 4 feet
using the Pythagorean Theorem...
8^2=4^2+h^2
64=16+h^2
h^2=48
h=4√3
Area=(1/2)*apothem*perimeter
A=(1/2)(4√3)(48)
A=2√3*48
A=96√3
A=96*1.7320508
A=166.277 square feet
So the area of the hexagon is 166.277 square feet using the triangle method, now I need to do the same thing only I need to divide it into two trapezoids. So first I did so and then I drew the height which created two little right triangles. Sum of total angle of a hexagon = (6–2) x 180 = 720.
Angle of each side = 720 / 6 = 120. And I tried finding the area of the triangle and later on finding the area of the trapezoid for the last step I added the two trapezoids areas to find my hexagon's area but no matter how much I try it won't measure 166.277 square feet as it did with the triangle method.
Can you please point at what I'm doing wrong? It's been 4 days and I'm still stuck at this, I have no clue how to solve it. I'm not asking anyone to do my homework, just kindly explain it to me, please!
Thanks in advance,
Emily