Work Shown:
A = area of the triangle
A = base*height/2
A = 9*7/2 = 63/2 = 31.5 ... see note1 below
B = area of rectangle
B = base*height
B = 9*3 = 27
C = area of parallelogram
C = base*height .... see note2 below
C = 9*6 = 54
If you're confused where I got the 6 from, check out the attached image below.
D = total area of the composite figure
D = A+B+C
D = 31.5 + 27 + 54
D = 112.5
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note1: The vertical component of the triangle is 9 units because this is part of the rectangle. The rectangle has opposite sides that are the same length. The parallelogram's vertical sides are 9 units long as shown by the single tickmark.
note2: a rectangle is essentially a special case of a parallelogram. In other words, a rectangle is a parallelogram with 4 right angles. So this is why the formula "area = base*height" shows up identical for both rectangles and parallelograms. Keep in mind that the height is always perpendicular to the base. You will not use the segments marked with double tickmarks.
Both claims are false. In fact, and
are one the multiplicative inverse of the other. This means, by definition of multiplicative inverse, that
So, it doesn't matter if is positive or negative: the multiplication of one number and its inverse will always be 1: for example,
Similarly, when you multiply two number, the sign of the product depends on the sign of the factors as follows:
So, the multiplication of two negative numbers is a positive number.