Question

In the figure below, triangle ZAX is equilateral and has perimeter 30. What is the exact area of the quadrilateral FLAX? Explain how you determined your answer.

Answer 1

86 units squared.

Explanation:

If the perimeter is 30 and it is an equilateral triangle, the means each side of the triangle is equal so they must all be 10 units longs. Since the line XA is part of the quadrilateral, lines FL and XA of the rectangle must be 10 units long. But we still don't know the length of the sides. Within the box are two right triangles, FZX and ZLA. We know the the length of the hypotenuse which is 10 units, and the base which is 5 units. Then we use the Pythagorean Theorem so find the length of the sides. After we do that we get about 8.6. Now we can multiply the length and width to get an area of 86.

Answer 2

$50\sqrt3$ (about 86)

Explanation:

because we know the equilateral triangle has a perimeter of 30, each side is 10. therefore, the base of the triangle (the length of FLAX) is 10. using the pythagorean theorem, we know that 5^2 + x^2 = 10^2 (where x is the width of FLAX). therefore, x^2 = 75 = x = the square root of 75; which when simplified is $5\sqrt3$. then, to find the area of FLAX we have l x w, so 10 times $5\sqrt3$ is $50\sqrt3$, or about 86.