| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.66 |
| Score | 0% | 73% |
If the base of this triangle is 9 and the height is 1, what is the area?
| 35 | |
| 25 | |
| 4\(\frac{1}{2}\) | |
| 40\(\frac{1}{2}\) |
The area of a triangle is equal to ½ base x height:
a = ½bh
a = ½ x 9 x 1 = \( \frac{9}{2} \) = 4\(\frac{1}{2}\)
If the area of this square is 4, what is the length of one of the diagonals?
| 5\( \sqrt{2} \) | |
| 2\( \sqrt{2} \) | |
| 7\( \sqrt{2} \) | |
| 3\( \sqrt{2} \) |
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 = \( \sqrt{a} \) = \( \sqrt{4} \) = 2
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 = 22 + 22
c2 = 8
c = \( \sqrt{8} \) = \( \sqrt{4 x 2} \) = \( \sqrt{4} \) \( \sqrt{2} \)
c = 2\( \sqrt{2} \)
If a = 2, b = 5, c = 6, and d = 1, what is the perimeter of this quadrilateral?
| 13 | |
| 18 | |
| 14 | |
| 21 |
Perimeter is equal to the sum of the four sides:
p = a + b + c + d
p = 2 + 5 + 6 + 1
p = 14
If a = c = 3, b = d = 9, what is the area of this rectangle?
| 15 | |
| 20 | |
| 27 | |
| 36 |
The area of a rectangle is equal to its length x width:
a = l x w
a = a x b
a = 3 x 9
a = 27
If angle a = 20° and angle b = 32° what is the length of angle c?
| 123° | |
| 128° | |
| 66° | |
| 107° |
The sum of the interior angles of a triangle is 180°:
180° = a° + b° + c°
c° = 180° - a° - b°
c° = 180° - 20° - 32° = 128°