ACT Math : Squares

Study concepts, example questions & explanations for ACT Math

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Example Questions

Example Question #1 : How To Find The Length Of The Side Of A Square

The circle inscribed inside Square  has circumference 16. To the nearest tenth, evaluate .

Possible Answers:

Correct answer:

Explanation:

The diameter of a circle that is inscribed inside a square is equal to its sidelength , so all we need to do is find the diameter of the circle - which is circumference 16 divided by :

.

 

Example Question #1 : How To Find The Length Of The Side Of A Square

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Refer to the above figure, which shows equilateral triangle  inside Square . Also, .

Quadrilateral  has area 100. Which of these choices comes closest to ?

Possible Answers:

Correct answer:

Explanation:

Let , the sidelength shared by the square and the equilateral triangle.

The area of  is

The area of Square  is .

By symmetry,  bisects the portion of the square not in the triangle, so the area of Quadrilateral  is half the difference of those of the square and the triangle. Since the area of Quadrilateral is 100, we can set up an equation:

Of the five choices, 20 comes closest.

Example Question #171 : Quadrilaterals

Find the length of the side of a square given its area is .

Possible Answers:

Correct answer:

Explanation:

To find side length, simply take the square root of the volume. Thus,

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