Area and Perimeter
Area and Perimeter
In this assessment, you will encounter a number of different questions that will assess both your understanding of mathematics and your ability to reason quantitatively.
Instructions
(Click to Read) Do not use a calculator in this assessment. You shouldn’t need one to answer these questions, and the extra practice with arithmetic (long division, multi-digit multiplication, etc.) will just make you a better math student!
Once you input your answer, click on “Check” to see immediate feedback about the question, including an explanation. You can also skip the question and come back to it later.
You may encounter different types of questions:
- Multiple Choice
- You will see several answer choices, but only one will be correct.
- Select the correct answer choice.
- Free-Response (Open-Ended)
- You will not see any answer choices, and only one answer is correct.
- Type your answer into the space provided.
- For fractions, input your answer as “#/#” without the quotation marks, replacing the # with numbers. For example:
- to input an answer of \(\frac{1}{2}\), type “1/2” without the quotation marks.
- For decimals less than 1, input your answer with a leading zero. For example:
- to input an answer of \(0.5\), type “0.5” without the quotation marks.
- For whole numbers, just type the number into the space provided. For example:
- to input an answer of \(5\), type “5” without quotation marks.
- Check-the-Box
- You will see several answer choices, but one or more may be correct.
- Select all correct answer choices.
Tips
(Click to Read) - These aren’t basic math questions – they’re tricky! Read closely and make sure you know what’s being asked.
- Do calculations on paper with a pencil. You don’t get extra credit for answering in your head!
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- 1 of 20Question1
If the area of a square is \(49\) cm\(^2\), what is the perimeter?
CorrectIncorrect - 2 of 20Question2
The perimeter of a rectangle is \(12\) inches. If the length and width are both integer values, which of the following could NOT be the area of the rectangle?
CorrectIncorrect - 3 of 20Question3
Using the information given, compare the quantity in Column A to the quantity in Column B.
Circle \(A\), which has a radius of \(2\) meters, sits inside Circle \(B\). The radius of Circle \(B\) is \(50\)% greater than the radius of Circle \(A\).
Column A
The area of the shaded region, in square meters
Column B
\(5\pi\)
CorrectIncorrect - 4 of 20Question4
Rectangles \(ABDC\) and Rectangle \(WXZY\) are similar, with \(WX\) equal to half of \(AB\). If \(AB=8\) and \(BD=4\), what is the area of the shaded region, in square units?
CorrectIncorrect - 5 of 20Question5
Using the information given, compare the quantity in Column A to the quantity in Column B.
The diameters of Circle \(L\) and Circle \(M\) are both equal to side \(AC\) of Rectangle \(ABDC\) below. The radius of Circle \(L\) is \(3\) feet.
Column A
Area of the shaded region, in square feet
Column B
\(72-9\pi\)
CorrectIncorrect - 6 of 20Question6
If triangle \(ACX\) is an isosceles right triangle, what is the perimeter of parallelogram \(ABDC\)?
CorrectIncorrect - 7 of 20Question7
Using the information given, compare the quantity in Column A to the quantity in Column B.
A rectangle with sides \(11\) and \(8\) has smaller rectangles each measuring \(2\) inches by \(3\) inches cut out from two of its corners, resulting in an octagon.
Column A
The perimeter of the octagon, in inches
Column B
\(36\) inches
CorrectIncorrect - 8 of 20Question8
Using the information given, compare the quantity in Column A to the quantity in Column B.
Square \(WXYZ\) is inscribed in Square \(ABCD\). \(W\), \(X\), \(Y\), and \(Z\) are the midpoints of each side of Square \(ABCD\).
Column A
The perimeter of Square \(ABCD\), if \(WX=\frac{4}{\sqrt{2}}\)
Column B
\(16\sqrt{2}\) units
CorrectIncorrect - 9 of 20Question9
The shaded figure, which is made up of \(12\) individual squares, has an area of \(108\) yards\(^2\). What is the perimeter of the shaded figure, in yards?
CorrectIncorrect - 10 of 20Question10
What is the area of isosceles trapezoid \(ABDC\) below?
CorrectIncorrect - 11 of 20Question11
A semi-circle is attached to Rectangle \(WXYZ\), as shown below. If \(WZ=8\), and the ratio of \(WX\) to \(WZ\) is \(3:2\), what is the perimeter of the figure?
CorrectIncorrect - 12 of 20Question12
The figure below shows four congruent squares, with the two outer squares overlapping the two inner squares. A vertex of each white square hits the midpoint of a gray square. If the perimeter of each square is \(24\) units, what is the area of the visible shaded region?
CorrectIncorrect - 13 of 20Question13
Circle \(C\) is inscribed in Square \(JKML\). If the radius of Circle \(C\) is \(4\) units, what is the area of the shaded region?
CorrectIncorrect - 14 of 20Question14
Using the information given, compare the quantity in Column A to the quantity in Column B.
A figure is formed from two congruent right triangles and a semi-circle. The hypotenuse of each triangle is \(10\) units and the base of each triangle is \(6\) units. If the perimeter of the outer figure is \(36+6\pi\), which column is greater?
Column A
Area of the entire figure
Column B
\(18\pi+30\)
CorrectIncorrect - 15 of 20Question15
Using the information given, compare the quantity in Column A to the quantity in Column B.
Column A The area of a square with perimeter of \(48\) cm
Column B The area of a rhombus with sides lengths of \(12\) cm
CorrectIncorrect - 16 of 20Question16
A figure (not shown) is made up of \(9\) individual squares. The each square has a side length of \(3\) inches. What is the area of the figure?
CorrectIncorrect - 17 of 20Question17
A trapezoid is shown. What is the area, in square units?
CorrectIncorrect - 18 of 20Question18
If all angles shown are \(90^{\circ}\), what is the area of the figure below?
CorrectIncorrect - 19 of 20Question19
If a regular hexagon has a side of \(6\) cm, what is its area?
CorrectIncorrect - 20 of 20Question20
A circle is inscribed in an equilateral triangle, as shown in the diagram. If the radius of the circle is \(3\) units and a side of the triangle measures \(6\sqrt3\), what is the area of the triangle?
CorrectIncorrect
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