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killasnake
09-11-2005, 05:33 PM
Hi I'm having the same problems once again. I just dont know where to start out with this problem. As you can tell I have lot of trouble with word problems.

An isosceles triangle is one where two sides have the same length and the third side has a possibly different length. Suppose you have an isosceles triangle where two sides have length "a" and the base has length "b" Then the height of that triangle is h=_______ The area of your triangle is A=______

and

Suppose you have an equilateral triangle with a height of h feet. Then its area is A=_______

and

Suppose you circumscribe a regular hexagon around a circle of radius . Thus the circle is inscribed the hexagon. The area of that hexagon is
A=______ square feet.


With these questions how do I solve them without any numbers?

stapel
09-11-2005, 05:58 PM
An isosceles triangle is one where two sides have the same length and the third side has a possibly different length. Suppose you have an isosceles triangle where two sides have length "a" and the base has length "b" [Find the height and area of the triangle.]
Draw the triangle. Label the sides. Draw the height line and label it "h".

This height line splits the original triangle into two congruent right triangles. The base (or half of it) provides one of the sides for each of these new triangles. Use the Pythagorean Theorem to find the value of "h" in terms of "a" and "b". Then plug this into the area formula, A = (1/2)bh.


Suppose you have an equilateral triangle with a height of h feet. [Find the area of the triangle.]
Draw the triangle. Draw the height line and label it as "h". Note that this line splits the original triangle into two right triangles.

An equilateral triangle has all equal angles. So what is the measure of the angles at the vertex from which you drew the height line? You have memorized the ratios for sides of this type of right triangle. Use those ratios to find an expression for the length of a side of the original triangle. Then plug this into the area formula.


Suppose you circumscribe a regular hexagon around a circle of radius [r]. Thus the circle is inscribed [inside] the hexagon. [Find the area of the hexagon.]
Draw the circle and the surrounding hexagon. Note that the circle touches the hexagon at the midpoint of each of the hexagon's sides. Note that the length of a segment from the center to this midpoint is "r".

Recall the "angle" measure of a circle. Draw lines from the center of the figure to each of the vertices of the hexagon. Note what sort of triangles you have just formed. Use your result from the previous exercise to complete this exercise.

Eliz.