SSAT Middle Level Math : SSAT Middle Level Quantitative (Math)

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

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Example Questions

Example Question #3 : Triangles

Triangle

 

What is the area of the above triangle?

Possible Answers:

Correct answer:

Explanation:

The two legs of a right triangle can serve as its base and its height. The area of the triangle is half the product of the two:

That is, the area is 3,000 square millimeters.

Example Question #3 : How To Find The Area Of A Triangle

Triangle

Note: Figure NOT drawn to scale.

The above triangle has an area of 450 square centimers. . What is  ?

Possible Answers:

Correct answer:

Explanation:

The area of a triangle is one half the product of its base and its height - in the above diagram, that means

.

Substitute , and solve for  :

Example Question #4 : Triangles

Q7

Find the area of the triangle.

Note: Figure not drawn to scale.

Possible Answers:

Correct answer:

Explanation:

To find the area of a triangle, multiply the base of the triangle by the height and then divide by two.

 

 

Example Question #4 : How To Find The Area Of A Triangle

Square

The quadrilateral in the above diagram is a square. What percent of it is white?

Possible Answers:

Correct answer:

Explanation:

The area of the entire square is the square of the length of a side, or

.

The area of the white right triangle is half the product of its legs, or

.

Therefore, the area of that triangle is 

of that of the entire square.

Example Question #3 : How To Find The Area Of A Triangle

Yard_2

Mr. Jones owns the isosceles-triangle-shaped parcel of land seen in the above diagram. He sells the parcel represented in red to his brother. What is the area of the land he retains?

Possible Answers:

Correct answer:

Explanation:

The area of a triangle is half the product of its base and its height, so Mr. Jones's parcel originally had area 

 square meters.

The portion he sold his brother, represented by the red right triangle, has area

 square meters.

Therefore, the area of the parcel Mr. Jones retained is 

 square meters.

Example Question #2 : Area Of A Triangle

Please use the following shape for the question. 5x3-adams-graphoc

What is the area of this shape?

Possible Answers:

Correct answer:

Explanation:

From this shape we are able to see that we have a square and a triangle, so lets split it into the two shapes to solve the problem. We know we have a square based on the 90 degree angles placed in the four corners of our quadrilateral. 

Since we know the first part of our shape is a square, to find the area of the square we just need to take the length and multiply it by the width. Squares have equilateral sides so we just take 5 times 5, which gives us 25 inches squared.

We now know the area of the square portion of our shape. Next we need to find the area of our right triangle. Since we know that the shape below the triangle is square, we are able to know the base of the triangle as being 5 inches, because that base is a part of the square's side. 

To find the area of the triangle we must take the base, which in this case is 5 inches, and multipy it by the height, then divide by 2. The height is 3 inches, so 5 times 3 is 15. Then, 15 divided by 2 is 7.5. 

We now know both the area of the square and the triangle portions of our shape. The square is 25 inches squared and the triangle is 7.5 inches squared. All that is remaining is to added the areas to find the total area. Doing this gives us 32.5 inches squared. 

Example Question #3 : Area Of A Triangle

What is the area of the triangle?

Question_11

Possible Answers:

Correct answer:

Explanation:

Area of a triangle can be determined using the equation:

Example Question #231 : Ssat Middle Level Quantitative (Math)

The hypotenuse of a right triangle is 25 inches; it has one leg 15 inches long. Give its area in square feet.

Possible Answers:

Correct answer:

Explanation:

The area of a right triangle is half the product of the lengths of its legs, so we need to use the Pythagorean Theorem to find the length of the other leg. Set :

The legs are 15 and 20 inches long. Divide both dimensions by 12 to convert from inches to feet:

 feet

 feet

Now find half their product:

 square feet

Example Question #1 : How To Find The Area Of A Triangle

Rectangles

Note: Figure NOT drawn to scale.

What percent of the above figure is green?

Possible Answers:

The correct answer is not given among the other choices.

Correct answer:

Explanation:

The area of the entire rectangle is the product of its length and width, or

.

The area of the right triangle is half the product of its legs, or

The area of the green region is therefore the difference of the two, or

.

The green region is therefore

of the rectangle.

Example Question #41 : Plane Geometry

Rectangles

Note: Figure NOT drawn to scale.

Refer to the above diagram. Give the ratio of the area of the green region to that of the white region.

Possible Answers:

The correct answer is not given among the other choices.

Correct answer:

Explanation:

The area of the entire rectangle is the product of its length and width, or

.

The area of the right triangle is half the product of its legs, or

The area of the green region is therefore the difference of the two, or

.

The ratio of the area of the green region to that of the white region is 

That is, 11 to 4.

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