| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.04 |
| Score | 0% | 61% |
Order the following types of angle from least number of degrees to most number of degrees.
right, acute, obtuse |
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acute, right, obtuse |
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acute, obtuse, right |
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right, obtuse, acute |
An acute angle measures less than 90°, a right angle measures 90°, and an obtuse angle measures more than 90°.
If the area of this square is 25, what is the length of one of the diagonals?
| 9\( \sqrt{2} \) | |
| 5\( \sqrt{2} \) | |
| \( \sqrt{2} \) | |
| 7\( \sqrt{2} \) |
To find the diagonal we need to know the length of one of the square's sides. We know the area and the area of a square is the length of one side squared:
a = s2
so the length of one side of the square is:
s = \( \sqrt{a} \) = \( \sqrt{25} \) = 5
The Pythagorean theorem defines the square of the hypotenuse (diagonal) of a triangle with a right angle as the sum of the squares of the other two sides:
c2 = a2 + b2
c2 = 52 + 52
c2 = 50
c = \( \sqrt{50} \) = \( \sqrt{25 x 2} \) = \( \sqrt{25} \) \( \sqrt{2} \)
c = 5\( \sqrt{2} \)
For this diagram, the Pythagorean theorem states that b2 = ?
c2 - a2 |
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c - a |
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c2 + a2 |
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a2 - c2 |
The Pythagorean theorem defines the relationship between the side lengths of a right triangle. The length of the hypotenuse squared (c2) is equal to the sum of the two perpendicular sides squared (a2 + b2): c2 = a2 + b2 or, solved for c, \(c = \sqrt{a + b}\)
The dimensions of this trapezoid are a = 5, b = 6, c = 7, d = 5, and h = 4. What is the area?
| 15 | |
| 10\(\frac{1}{2}\) | |
| 22 | |
| 13\(\frac{1}{2}\) |
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(6 + 5)(4)
a = ½(11)(4)
a = ½(44) = \( \frac{44}{2} \)
a = 22
Which of the following is not true about both rectangles and squares?
all interior angles are right angles |
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the lengths of all sides are equal |
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the area is length x width |
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the perimeter is the sum of the lengths of all four sides |
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).