Plane Geometry

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SSAT Middle Level Quantitative › Plane Geometry

Questions 1 - 10
1

The ratio of the perimeter of one square to that of another square is . What is the ratio of the area of the first square to that of the second square?

Explanation

For the sake of simplicity, we will assume that the second square has sidelength 1; Then its perimeter is , and its area is .

The perimeter of the first square is , and its sidelength is . The area of this square is therefore .

The ratio of the areas is therefore .

2

A square is 9 feet long on each side. How many smaller squares, each 3 feet on a side can be cut out of the larger square?

Explanation

Each side can be divided into three 3-foot sections. This gives a total of squares. Another way of looking at the problem is that the total area of the large square is 81 and each smaller square has an area of 9. Dividing 81 by 9 gives the correct answer.

3

The area of the square is 81. What is the sum of the lengths of three sides of the square?

Explanation

A square that has an area of 81 has sides that are the square root of 81 (side2 = area for a square). Thus each of the four sides is 9. The sum of three of these sides is .

4

The ratio of the perimeter of one square to that of another square is . What is the ratio of the area of the first square to that of the second square?

Explanation

For the sake of simplicity, we will assume that the second square has sidelength 1; Then its perimeter is , and its area is .

The perimeter of the first square is , and its sidelength is . The area of this square is therefore .

The ratio of the areas is therefore .

5

A square is 9 feet long on each side. How many smaller squares, each 3 feet on a side can be cut out of the larger square?

Explanation

Each side can be divided into three 3-foot sections. This gives a total of squares. Another way of looking at the problem is that the total area of the large square is 81 and each smaller square has an area of 9. Dividing 81 by 9 gives the correct answer.

6

The area of the square is 81. What is the sum of the lengths of three sides of the square?

Explanation

A square that has an area of 81 has sides that are the square root of 81 (side2 = area for a square). Thus each of the four sides is 9. The sum of three of these sides is .

7

The area of the square is 81. What is the sum of the lengths of three sides of the square?

Explanation

A square that has an area of 81 has sides that are the square root of 81 (side2 = area for a square). Thus each of the four sides is 9. The sum of three of these sides is .

8

What is the length of a line with endpoints and .

Explanation

To find the length of this line, you can subtract to get . Since the y-coordinates are the same, you don't have to take any vertical direction into account. Therefore, you only look at the x-coordinates!

9

What is the area of the triangle?

Question_11

Explanation

Area of a triangle can be determined using the equation:

10

What is the length of a line segment with end points and ?

Explanation

The length of a line segment can be determined using the distance formula:

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