MHB What is the area of an isosceles triangle with side lengths 6, 6, and 4?

  • Thread starter Thread starter Elissa89
  • Start date Start date
  • Tags Tags
    Area Triangle
AI Thread Summary
The area of the isosceles triangle with side lengths 6, 6, and 4 is calculated using two methods. First, by splitting the triangle, the height is found to be 4√2, leading to an area of 8√2. The second method, Heron's formula, confirms this area calculation, yielding the same result of 8√2. Both methods validate the correctness of the area calculation. The final area of the triangle is 8√2.
Elissa89
Messages
52
Reaction score
0
Side lengths are a=6, b=6, c=4. Find the area

A=1/2*b*h

I split the triangle in half to find the height. Since the base is 4, that divided the base into 2:

2^2+h^2=6^2

4+h^2=36

h^2=32

h=4*sqrt(2)
===========

1/2*4*4*sqrt(2)=area of 8*sqrt(2)

Did I do this correctly? I do not have an answer key to the study guide I was given.
 
Mathematics news on Phys.org
Let's check your answer using Heron's formula...the semi-perimeter \(s\) is 8, hence:

$$A=\sqrt{8(8-6)(8-6)(8-4)}=\sqrt{2^7}=8\sqrt{2}\quad\checkmark$$
 
Seemingly by some mathematical coincidence, a hexagon of sides 2,2,7,7, 11, and 11 can be inscribed in a circle of radius 7. The other day I saw a math problem on line, which they said came from a Polish Olympiad, where you compute the length x of the 3rd side which is the same as the radius, so that the sides of length 2,x, and 11 are inscribed on the arc of a semi-circle. The law of cosines applied twice gives the answer for x of exactly 7, but the arithmetic is so complex that the...
Thread 'Video on imaginary numbers and some queries'
Hi, I was watching the following video. I found some points confusing. Could you please help me to understand the gaps? Thanks, in advance! Question 1: Around 4:22, the video says the following. So for those mathematicians, negative numbers didn't exist. You could subtract, that is find the difference between two positive quantities, but you couldn't have a negative answer or negative coefficients. Mathematicians were so averse to negative numbers that there was no single quadratic...
Thread 'Unit Circle Double Angle Derivations'
Here I made a terrible mistake of assuming this to be an equilateral triangle and set 2sinx=1 => x=pi/6. Although this did derive the double angle formulas it also led into a terrible mess trying to find all the combinations of sides. I must have been tired and just assumed 6x=180 and 2sinx=1. By that time, I was so mindset that I nearly scolded a person for even saying 90-x. I wonder if this is a case of biased observation that seeks to dis credit me like Jesus of Nazareth since in reality...

Similar threads

Replies
5
Views
2K
Replies
1
Views
990
Replies
1
Views
2K
Replies
3
Views
2K
Replies
1
Views
1K
Replies
20
Views
3K
Replies
3
Views
1K
Back
Top