| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.30 |
| Score | 0% | 66% |
If the area of this square is 1, what is the length of one of the diagonals?
| 2\( \sqrt{2} \) | |
| 3\( \sqrt{2} \) | |
| 4\( \sqrt{2} \) | |
| \( \sqrt{2} \) |
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 = \( \sqrt{a} \) = \( \sqrt{1} \) = 1
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 = 12 + 12
c2 = 2
c = \( \sqrt{2} \)
The dimensions of this trapezoid are a = 5, b = 8, c = 8, d = 2, and h = 3. What is the area?
| 15 | |
| 37\(\frac{1}{2}\) | |
| 10 | |
| 12 |
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(8 + 2)(3)
a = ½(10)(3)
a = ½(30) = \( \frac{30}{2} \)
a = 15
If side a = 4, side b = 5, what is the length of the hypotenuse of this right triangle?
| \( \sqrt{32} \) | |
| \( \sqrt{34} \) | |
| \( \sqrt{41} \) | |
| \( \sqrt{17} \) |
According to the Pythagorean theorem, the hypotenuse squared is equal to the sum of the two perpendicular sides squared:
c2 = a2 + b2
c2 = 42 + 52
c2 = 16 + 25
c2 = 41
c = \( \sqrt{41} \)
If a = c = 8, b = d = 6, and the blue angle = 63°, what is the area of this parallelogram?
| 72 | |
| 3 | |
| 48 | |
| 18 |
The area of a parallelogram is equal to its length x width:
a = l x w
a = a x b
a = 8 x 6
a = 48
If a = c = 8, b = d = 2, what is the area of this rectangle?
| 6 | |
| 7 | |
| 16 | |
| 63 |
The area of a rectangle is equal to its length x width:
a = l x w
a = a x b
a = 8 x 2
a = 16