We all know the usual formula for the area of a triangle:

(1) area A = 1/2*base*height.^{ }_{ }

There are two other formulas that are fairly common.^{ }_{ }
You can find the area of a triangle when you know the lengths of the three sides.^{ }_{ }
Heron of Alexandria (born about 10 in (possibly) Alexandria, Egypt; died about 75) proved Heron's formula for a triangle with sides a, b, and c:^{ }_{ }

(3) Suppose you know the measure of one angle A in the triangle, and the length of the two sides adjacent to (on either side of) the angle, b and c.^{ }_{ } Then area of the triangle is 1/2*b*c*sin A. ^{ }_{ } (See below for a proof of this formula.)^{ }_{ }

Let's try out these three formulas on three congruent triangles and see if we get (approximately) the same area in all three cases.^{ }_{ }

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