Question 1205402: A group of four Grade 9 students are to play a baseball game. Roughly, they create a baseball field in a diamond shape and represent each base as A, B, C, and D. AB and AD are the consecutive adjacent equal sides so as to BC and DC and AC ⊥ BD where BD = 24 meters. If the distance of points A to B is 13 meters while points B to C is 15 meters, find the area of the created baseball field. Provide Illustration, Working Equation, Solution, and Answer.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! here's my diagram.
you have triangle dcb formed by connecting right triangle dck and bck at ck.
you have triangle dab formed by connecting right triangle dak and bak at ck.
by pythagorus, a^2 + b^2 = c^2
a is one of the legs of the triangle and b is the other leg of the triangle and c is the hypotenuse.
for triangle dck, a would be dk and b would be ck and c would be dc
a^2 + b^2 = c^2 becomes 12^2 + [ck]^2 = 15^2
solve for [ck]^2 to get [ck]^2 = 15^2 - 12^2 = 81
take the square root of both sides of the equation to get ck = 9
similarly, ak = 5 because 13^2 - 12^2 = 25 and square root of 25 is 5.
the area of a triangle is equal to 1/2 * the base * the height.
for triangle dcb, that becomes area = 1/2 * 24 * 9 = 108
for triangle dab, that becomes area = 1/2 * 24 * 5 = 60
the total area of the baseball diamond is equal to 168.
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