Quadrilaterals

Words of “Wiz-dom”-There’s nothing difficult about the math calculations related to quadrilaterals (four sided figures) on the SAT or ACT. They are about perimeters and areas (or partial areas). The test writer just makes them mysterious by doing unusual things like embedding circles or overlapping two or more figures or requiring you to complete diagrams by drawing lines that aren’t part of the original figures.

Let’s clear some cobwebs since it’s been awhile since you used these introductory geometry skills.

Squares:

All of the following questions refer to square ABCD.

What is the size of the angles at each corner? Answer #1

What is true about the ratios of the lengths of the sides? Answer #2

What is formed by drawing a diagonal (be specific)? Answer #3

If AB is 3, what is the perimeter? Answer #4

If AD is 5, what is the area? Answer #5

If CD is 4, what is the area of a triangle formed by the diagonal AC? Answer #6

If AD is 1, what is the length of BD? Answer #7

Words of “Wiz-dom”–It is very valuable to remember that when you draw a diagonal in a square that it is the hypotenuse of a 45:45:90 triangle which you will see on the “cheat sheet.”  Take a look at it and you’ll see the proportions of the sides.  Whenever you see the square root of 2 on a hypotenuse it will be on one of these triangles.  Recognizing it is so will greatly improve your speed on doing the question.

Rectangles:

All of the following questions refer to rectangle ABCD.

What is the size of the angles at each corner? Answer #8

What is true about the ratios of the lengths of the sides? Answer #9

What does drawing a diagonal form? Be specific. Answer #10

If AB=3 and BC=6, what is the perimeter? the area? What does drawing an altitude at the midpoint of AD form? What is the sum of their perimeters? Answer #11

If a diagonal is drawn and it is twice the height, what is true about the resulting triangle? Answer #12

Using this rectangle, explain why the formula for the area of a triangle works. Answer #13

Parallelograms:

All of the following questions refer to parallelogram ABCD.

What is true about the size of the angles? Answer #14

What is true about the ratios of the lengths of the sides?  Answer #15

What is formed by drawing diagonals? Answer #16

What is the perimeter of the parallelogram? Answer #17

What does drawing an altitude DOWN from B form? Answer #18

What is the area of the parallelogram, if the altitude intersects AD 3 units to the right of A? Answer #19

If you cut off the “tail” using the altitude and attach AB to CD, what shape do you get? Answer #20

Why do you use the altitude and not the length of AB to calculate the area of ABCD? Answer #21

Sample Questions

15.  What is the area of parallelogram ABCD?

(A)
(B) 240
(C)
(D) 120
(E) 

Answer Question #15

6. In the square ABCD, the length of the diagonal is . What is the perimeter of the square?

(A) 2
(B) 4
(C)
(D) 8
(E) 16

Answer Question #6

14.  If the area of the rectangle ABCD is 112, what is the value of x?

(A) 4
(B) 5
(C) 6
(D) 7
(E) 8

Answer Question #14

Polygon Angles

The sum of the angles in any polygon follows a specific pattern.  Triangles have 180 degrees, quadrilaterals have 360 degrees, pentagons (5 sides) have 540 degrees, and so on.  The pattern is a simple one of adding an additional 180 degrees each time there is an extra side.  You can also use the formula:

180(n-2)= number of degrees

Where n is the number of sides.

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