Isosceles Triangle Another important type of triange is the isosceles triangle. An isosceles triangle has two equal sides and equal angles at the base of (or opposite) each of the equal sides. Isosceles Triangle = 2 sides and 2 opposite angles equal. In the figure below, the two upright sides are equal as are the angles opposite them, or at their bases.
To find the are of this triangle, you must first find the height, or altitude. The altitude of a triangle is the perpendicular distance from the base to the opposite vertex. A vertex is the point where two sides of a figure meet. You can choose any side for the base. Altitude = perpendicular distance from base to the opposite vertex
For the triangle above we will choose the bottom for the base. To find the altitude, we will draw a line perpendicular to the base. Because the angles on each side of the line are 90 degrees, and the opposite angles are the same, we know tht the two angles at the top are the same and therefore the two triangles are identical. In this case the altitude bisects the base. To calculate the altitude, consider the right-angle triangle on the right. Base = 1/2 * 16 = 8 Hypotenuse = 10 Using the Pythagorean Theorem, 102 = 82 + altitude2 100 = 64 + altitude2 altitude2 = 36, altitude = 6 Now we can calculate the area = 1/2 base * altitude = 1/2*16*6 = 48
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