 The My College Options® Resource Center provides up to date news and information for students and parents. # ACT Math Skill Review: Quadrilaterals

The ACT will test your knowledge of several types of four-sided figures (quadrilaterals). Indeed, you will be expected to solve many types of questions utilizing the information these figures offer. The most common four-sided figures are the rectangle and the square, followed by the parallelogram and the trapezoid. Note: for any four-sided (or three-sided, or more-sided) figure, the perimeter is the sum of the lengths of all the sides.

Let’s take a look at the most common types of quadrilaterals, starting with the most general, the parallelogram.

#### The Parallelogram Parallelogram Facts:

• A parallelogram is a four-sided figure.
• Both pairs of opposite sides are parallel and equal.
• Both pairs of opposite angles are equal.
• The area of a parallelogram is its base times its height (Area of a parallelogram = bh), but due to its shape, the height of the parallelogram is not always equal to one of its sides.
• To find the height of a parallelogram, you must draw a perpendicular line from the base to the top of the figure.

#### The Rectangle Rectangle Facts

• A rectangle is a parallelogram.
• All four interior angles are equal to 90°.
• Opposite sides of a rectangle are equal.
• The diagonal of a rectangle makes two equal right triangles.
• The Pythagorean Theorem can be used to figure out details regarding the length of sides or the diagonal, depending on what information you’re given.
• The area of a rectangle is its length times its width (Area of a rectangle = lw).
• The perimeter of a rectangle is the sum of the lengths of its sides, or twice its length plus twice its width (2l + 2w)

#### The Square Square Facts:

• A square is a type of rectangle whose four sides are equal in length.
• The diagonal of a square makes two 45°-45°-90° triangles with the sides of the square.
• You can figure out the length of the sides from the length of the diagonal and vice versa.
• The area of a square is equal to the square of its side (Area of a square = s2). (Since the square is a rectangle, the area of a square is also length times width. However, since each side (s) is the same, the area of a square is usually represented as s2.)
• The perimeter of a square is the sum of the lengths of its sides, or four times the length of its side (4s).

#### Trapezoids Trapezoid Facts

• A trapezoid is a quadrilateral that only has one pair of parallel sides.
• The easiest way to find the area of a trapezoid is to divide it into two triangles and a rectangle, figure out the areas of the individual pieces and add the results together to find the area of the whole figure.

#### Examples 1. The correct answer is B. If a question describes a shape but doesn’t provide you with a picture, it is usually helpful to draw it out. Here’s an example of what you’d end up with (note: it doesn’t have to be exact so don’t belabor it!). If we recall our parallelogram facts, opposite interior angles are equal. Thus, angle C is also 35°. Drawing it out helps to see that angles A and C are opposite. Angles B and D are also equal. Since all the angles add up to 360°,  B + D must equal 360 – (35 + 35). Thus, B + D = 290 and B and D both equal 145°. Notice that 145° and 290° both make an appearance in the answer choices as well, making it easy to make a careless mistake on a relatively straightforward problem.

2. The correct answer is H. In any quadrilateral, the interior angles must add up to 360°. We have values for two of the angles (19° and 89°) which together total 108°. Thus, there are 360° – 108°, or 252°  unaccounted for. These 252°  can be divided many ways, as long as the sum remains unchanged. The only answer choice that adds up to 252 is choice H. Thank you for visiting MyCollegeOptions.org

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