SSAT Upper Level Math : How to find the area of a square

Study concepts, example questions & explanations for SSAT Upper Level Math

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Example Questions

Example Question #11 : How To Find The Area Of A Square

A square and a circle have the same area. The circle has diameter 10. Which expression is equal to the length of one side of the square?

Possible Answers:

Correct answer:

Explanation:

A circle with diameter 10 has radius half this, or 5. The area of the circle can be found using the formula

,

setting :

.

The square also has this area. The length of one side of this square is equal to the square root of this, which is

Simplify this by breaking the radicand, as follows:

Example Question #61 : Areas And Perimeters Of Polygons

Right triangle 6

A square has the same area as the above right triangle. Give the length of one side of the square.

Possible Answers:

Correct answer:

Explanation:

The area of a right triangle is equal to half the product of the lengths of its legs. Since we know the lengths of one leg and the hypotenuse, we can calculate the length of the other leg using the Pythagorean Theorem. We can use this form:

Setting  and  equal to the lengths of the hypotenuse and the known leg - 13 and 5, respectively:

The area of the above triangle is

The square also has this area. The length of one side of this square is equal to the square root of this, which is .

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