if a white birch tree and a pin oak tree each now have a diameter of 111 foot, which of the following will be closest to the dif
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Answer: 54 cm²
Step-by-step explanation: In this problem, we're asked to find the area of the trapezoid shown. A trapezoid is a quadrilateral with one pair of parallel sides.
The formula for the area of a trapezoid is shown below.
The <em>b's</em> represent the bases which are the parallel sides and <em>h</em> is the height.
So in the trapezoid shown, the bases are 6 cm and 12 cm and the height is 6 cm. Plugging this information into the formula, we have .
Next, the order of operations tell us that we must simplify inside the parentheses first. 6 cm + 12 cm is 18 cm and we have .
is 9 cm and we have 9 cm · 6 cm of 54 cm²
So the area of the trapezoid shown is 54 cm².
In order to determine the vertex of this, you can complete the square. To do that, first set the equation equal to 0, then move the -35 over to the other side by adding. That gives us 
. Now we can complete the square. Do this by taking half of the linear term, squaring it, and adding it in to both sides. Our linear term is 2x. Half of 2 is 1, and 1 squared is 1. So we add 1 to both sides, creating something that looks like this: 
. We will do the math on the right and get 36, and the left will be expressed as the perfect square binomial we created by doing this whole process. 
. Now move the 36 over by subtraction and set it back to equal y and your vertex is apparent. It is (1, -36). You find the x-intercepts when y = 0. That means you need to set your original equation equal to zero and factor it. The easiest, surest way to do this is to use the quadratic formula. Doing that gives us x values of 7 and -5. And you're done!