SOLUTION: Find the area of the shaded figure, rounded to two decimals. (Assume x = 2 and y = 6.) http://www.webassign.net/sprecalc6/6-6-034-alt.gif link to figure

Algebra ->  Trigonometry-basics -> SOLUTION: Find the area of the shaded figure, rounded to two decimals. (Assume x = 2 and y = 6.) http://www.webassign.net/sprecalc6/6-6-034-alt.gif link to figure      Log On


   



Question 1080607: Find the area of the shaded figure, rounded to two decimals. (Assume x = 2 and y = 6.)

http://www.webassign.net/sprecalc6/6-6-034-alt.gif
link to figure

Found 3 solutions by Boreal, MathLover1, MathTherapy:
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
If y is the side
the area is 5 parts, the area of the base, x^2=4, plus 4 times the area of the faces. The height of a face is a straight line drawn to bisect the base. The triangle formed has hypotenuse 6, base 1 (bisected), and altitude sqrt (35). (Pythagorean theorem 1^2+x^2=6^2)
The area of each face is (1/2)bh=(1/2)*2* sqrt (35)=sqrt (35)
There are 4 of them so the area of the faces collectively is 4 sqrt (35)=23.66
Add to that the 4 above and the area is 27.66.

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
given: x+=+2 and y+=+6 and two equilateral triangles
You have two equilateral triangles (you know this since two of the three sides have a length of "y" in each triangle.
Both triangles are the same.
To get the area, we need to know the height. We know the base is x=2, but not the height.
Altitude of the shaded isosceles triangle:
h%5E2+=+y%5E2+%2B+%28x%2F2%29%5E2
h+=+sqrt%28y%5E2+%2B+%28x%2F2%29%5E2%29..........x=2 and y=6
h+=+sqrt%286%5E2+%2B+%282%2F2%29%5E2%29
h+=+sqrt%2836%2B+1%29
h+=+sqrt%2837%29
h+=+6.08

Surface area of the shaded one isosceles triangle:
A%5B1%5D=+%281%2F2%29hx
Surface area of the whole shaded figure:
A+=+2A%5B1%5D
so,
A+=++2%281%2F2%29hx
A+=+hx.............plug in values for h+=+6.08 and x=2
A+=+6.08%2A2
A+=+12.16

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

Find the area of the shaded figure, rounded to two decimals. (Assume x = 2 and y = 6.)

http://www.webassign.net/sprecalc6/6-6-034-alt.gif
link to figure
Height of 1 of the triangles: sqrt%2835%29, so area = matrix%281%2C3%2C+%281%2F2%29+%2A+b+%2A+height%2C+%22=%22%2C+sqrt%2835%29%29
Triangles are congruent, so area of the 2 triangles is: