### SAT Prep Class: Finding the Area of a Triangle

Check out Bas Rutten's Liver Shot on MMA Surge: http://bit.ly/MMASurgeEp1 SAT Prep Question #12 ? Question: In this equilateral triangle, one side length is equal to 6. What is the area (A) of the triangle?? To solve this problem, it's important to remember that the triangle is equilateral. Therefore, all three sides are equal.? You should also know the formula for the area of a triangle. The area is equal to one half the base of the triangle times the vertical height of the triangle, or A=1/2(b)(h).? Since all sides are equal, the base is the same as the side labeled 6. You know one part of the equation but you still need to figure out the height of the triangle.? The vertical height of the triangle is represented on the figure as the line dropping straight down from the top vertex. You will need to solve for this value.? Solve the Problem 1. The first step is to recognize the right triangle that's created by the vertical height.? Since this is a right triangle, you can use the Pythagorean theorem to find the value of the vertical height and then ?plug it into the equation for the area.? 2. To do this, you'll need to find the length of the base of the right triangle. You already know that the base of the equilateral triangle is 6, since all the sides are the same. The vertical height splits the base exactly in half. Therefore, the base of the right triangle is half of 6, or 3.? 3. Now that you know two sides of the right triangle, you can plug them into the theorem to solve for the last side, which is the vertical height. Since a?+b?=c?, your equation will read:? h?+3?=6? Simplify this equation to get:?h? =6?-3?. This becomes?h? =36-9, or?h?=27.? To?find "h," you need to take the square root of both sides. To find the square root of 27, write the equation as h=√9x3. The square root of 9 is 3, so the equation can be simplified to h=3√3.? 4. Now that you know the height of the triangle, you can plug it into the area equation and solve for the area.? The area equation now reads A=1/2(6)(3√3). You can simplify this to A=3x3√3=9√3. It's ok to leave the answer in radical form.? A=?9√3 Read more by visiting our page at: http://www.mahalo.com/courses/sat-math-prep/practice-questions/area-of-a-triangle/

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