| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.74 |
| Score | 0% | 55% |
If a = c = 4, b = d = 5, and the blue angle = 72°, what is the area of this parallelogram?
| 12 | |
| 20 | |
| 21 | |
| 4 |
The area of a parallelogram is equal to its length x width:
a = l x w
a = a x b
a = 4 x 5
a = 20
If side a = 6, side b = 3, what is the length of the hypotenuse of this right triangle?
| \( \sqrt{45} \) | |
| \( \sqrt{20} \) | |
| \( \sqrt{37} \) | |
| \( \sqrt{50} \) |
According to the Pythagorean theorem, the hypotenuse squared is equal to the sum of the two perpendicular sides squared:
c2 = a2 + b2
c2 = 62 + 32
c2 = 36 + 9
c2 = 45
c = \( \sqrt{45} \)
The dimensions of this trapezoid are a = 6, b = 9, c = 8, d = 2, and h = 5. What is the area?
| 18 | |
| 35 | |
| 27\(\frac{1}{2}\) | |
| 22 |
The area of a trapezoid is one-half the sum of the lengths of the parallel sides multiplied by the height:
a = ½(b + d)(h)
a = ½(9 + 2)(5)
a = ½(11)(5)
a = ½(55) = \( \frac{55}{2} \)
a = 27\(\frac{1}{2}\)
Which of the following is not true about both rectangles and squares?
the perimeter is the sum of the lengths of all four sides |
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the area is length x width |
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all interior angles are right angles |
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the lengths of all sides are equal |
A rectangle is a parallelogram containing four right angles. Opposite sides (a = c, b = d) are equal and the perimeter is the sum of the lengths of all sides (a + b + c + d) or, comonly, 2 x length x width. The area of a rectangle is length x width. A square is a rectangle with four equal length sides. The perimeter of a square is 4 x length of one side (4s) and the area is the length of one side squared (s2).
Solve -7c + 4c = 7c + 9z - 1 for c in terms of z.
| -\(\frac{1}{4}\)z + 2\(\frac{1}{4}\) | |
| \(\frac{1}{2}\)z - 3\(\frac{1}{2}\) | |
| -\(\frac{5}{14}\)z + \(\frac{1}{14}\) | |
| -\(\frac{6}{11}\)z + \(\frac{3}{11}\) |
To solve this equation, isolate the variable for which you are solving (c) on one side of the equation and put everything else on the other side.
-7c + 4z = 7c + 9z - 1
-7c = 7c + 9z - 1 - 4z
-7c - 7c = 9z - 1 - 4z
-14c = 5z - 1
c = \( \frac{5z - 1}{-14} \)
c = \( \frac{5z}{-14} \) + \( \frac{-1}{-14} \)
c = -\(\frac{5}{14}\)z + \(\frac{1}{14}\)