| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.28 |
| Score | 0% | 66% |
If a = 1, b = 6, c = 8, and d = 1, what is the perimeter of this quadrilateral?
| 16 | |
| 26 | |
| 11 | |
| 22 |
Perimeter is equal to the sum of the four sides:
p = a + b + c + d
p = 1 + 6 + 8 + 1
p = 16
A(n) __________ is to a parallelogram as a square is to a rectangle.
quadrilateral |
|
triangle |
|
trapezoid |
|
rhombus |
A rhombus is a parallelogram with four equal-length sides. A square is a rectangle with four equal-length sides.
Which of the following statements about a parallelogram is not true?
the area of a parallelogram is base x height |
|
opposite sides and adjacent angles are equal |
|
a parallelogram is a quadrilateral |
|
the perimeter of a parallelogram is the sum of the lengths of all sides |
A parallelogram is a quadrilateral with two sets of parallel sides. Opposite sides (a = c, b = d) and angles (red = red, blue = blue) are equal. The area of a parallelogram is base x height and the perimeter is the sum of the lengths of all sides (a + b + c + d).
What is 9a5 - 2a5?
| 7a5 | |
| 7a10 | |
| 11a10 | |
| 18a10 |
To combine like terms, add or subtract the coefficients (the numbers that come before the variables) of terms that have the same variable raised to the same exponent.
9a5 - 2a5 = 7a5
If the area of this square is 81, what is the length of one of the diagonals?
| 9\( \sqrt{2} \) | |
| \( \sqrt{2} \) | |
| 6\( \sqrt{2} \) | |
| 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 = \( \sqrt{a} \) = \( \sqrt{81} \) = 9
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 = 92 + 92
c2 = 162
c = \( \sqrt{162} \) = \( \sqrt{81 x 2} \) = \( \sqrt{81} \) \( \sqrt{2} \)
c = 9\( \sqrt{2} \)