Triangle A C D is shown. Point B is near the center of the triangle. Angle A C D is bisected by line segment C B. Lines are draw
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Answer:
Step-by-step explanation:
<u>Congruent Triangles</u>
The figure shows two triangles FCD and FED. One of their sides is the radius of the circle, they both form a 90° angle with the line CD and ED and they share the same segment FD.
Thus, both triangles are congruent and we have the length of a side (12 units), one common side (the hypotenuse) and one unknown leg that must be equal. Therefore
Solving
The required side FD is the hypotenuse of any of the triangles. The unknown leg can be calculated by
Or
Thus
Solving
There are three parts to this figure: a rectangle and two triangles that are congruent.
We'll add together the area for each to get the total area.
We'll start by finding the area of the rectangle. We don't know its length, so we need to find the bases of the triangles and add them together.
We know that . Substitute and solve for
:
Now, double this to get the total length of the rectangle, which is inches.
The area of the rectangle is equal to its length times its height:
Now, we'll find the area of one of the triangles and double it since they're congruent.
The area of a triangle is one-half of its base times its height, which we then double.
The and the
cancel each other out.
Substitute and solve:
Finally, add the rectangle's area to the two triangles' area.