ATI TEAS Guide To Math  Perimeters, Surface Area, Area Question Review
ATI TEAS Math Geometry
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Question 1 of 8
1. Question
A circular garden has a diameter of 140 yards. What is the area of the garden?
Correct
The formula for area of a circle is A = πr(2). If the diameter is 140 yards, then the radius is 70 yards. So A = π70(2) = 4,900π. Since the answer choices are far apart from each other, you can estimate π = 3 and 4,900 x 3 = 14,700. Since π is a bit larger than 3, the real answer will be a bit larger than 14,700. Choice A is close and the other choices are far too large.
Incorrect
The formula for area of a circle is A = πr(2). If the diameter is 140 yards, then the radius is 70 yards. So A = π70(2) = 4,900π. Since the answer choices are far apart from each other, you can estimate π = 3 and 4,900 x 3 = 14,700. Since π is a bit larger than 3, the real answer will be a bit larger than 14,700. Choice A is close and the other choices are far too large.

Question 2 of 8
2. Question
The area of a square patio is 289 square feet. If the owner wants to put a border around the patio, what length of border will be needed?
Correct
To answer this question, you will need to find the perimeter of the patio. If the area is 289 and the patio is square, take the square root of 289 to find the length of each side. √289 = 17. TO find the perimeter, add up the lengths of the sides: 4 x 17 = 68.
Incorrect
To answer this question, you will need to find the perimeter of the patio. If the area is 289 and the patio is square, take the square root of 289 to find the length of each side. √289 = 17. TO find the perimeter, add up the lengths of the sides: 4 x 17 = 68.

Question 3 of 8
3. Question
The triangle is an equilateral triangle with a perimeter of 9. What is the length of one side?
Correct
An equilateral triangle has sides of equal length. If the perimeter is 9, then divide by 3 sides to get a length of 3 for each side.
Incorrect
An equilateral triangle has sides of equal length. If the perimeter is 9, then divide by 3 sides to get a length of 3 for each side.

Question 4 of 8
4. Question
What is the area of a circle with a diameter of 8?
Correct
If the diameter is 8, then the radius is 4. Use the formula A = πr^{2}. A = π4^{2} = 16π.
Incorrect
If the diameter is 8, then the radius is 4. Use the formula A = πr^{2}. A = π4^{2} = 16π.

Question 5 of 8
5. Question
The area of triangle A is 4. The height of triangle B is twice that of triangle A, and the length of the base of triangle B is the same as that if triangle A. What is the area of triangle B?
Correct
Let the height of triangle A = h and the base = b. Since the area of triangle A is 4, we can say 4 = 1/2 bh. Since the height of triangle B is twice the height of triangle A, and the length of the base is the same, the area of triangle B is 1/2 b(2h) = bh. If the area of A is 4 = 1/2 bh and the area of B is bh, then B is twice the area of A. If A = 4, then B = 8.
Incorrect
Let the height of triangle A = h and the base = b. Since the area of triangle A is 4, we can say 4 = 1/2 bh. Since the height of triangle B is twice the height of triangle A, and the length of the base is the same, the area of triangle B is 1/2 b(2h) = bh. If the area of A is 4 = 1/2 bh and the area of B is bh, then B is twice the area of A. If A = 4, then B = 8.

Question 6 of 8
6. Question
A swimming pool is 35 feet long and 12 feet wide. What is the perimeter of the pool?
Correct
The perimeter will be twice the length plus twice the width, so (35 x 2) + (12 x 2) = 94.
Incorrect
The perimeter will be twice the length plus twice the width, so (35 x 2) + (12 x 2) = 94.

Question 7 of 8
7. Question
Rectangle 1 has a length of L and a width of W. Rectangle 2 has a length of L and a width of 2W. Which of the following statements is true?
Correct
The area of Rectangle 1 is L x W. The area of Rectangle 2 is L x 2W or 2(L x W). Rectangle 2 is twice as big as Rectangle 1, so the area of Rectangle 1 is half that of Rectangle 2.
Incorrect
The area of Rectangle 1 is L x W. The area of Rectangle 2 is L x 2W or 2(L x W). Rectangle 2 is twice as big as Rectangle 1, so the area of Rectangle 1 is half that of Rectangle 2.

Question 8 of 8
8. Question
A courtyard measuring 7 yards by 9 yards will be tiled. How many 12inch square tiles will be required to cover the courtyard?
Correct
First find the area of the courtyard. 9 x 7 = 63 yards^{2}. The tiles are 12inch squares, so you need to convert that to yards. 36 inches = 1 yard, so 12 inches = 1/3 yard. Write an equation to find the number of tiles: t x 1/3 = 63. Multiply both sides by 3 to get t = 189.
Incorrect
First find the area of the courtyard. 9 x 7 = 63 yards^{2}. The tiles are 12inch squares, so you need to convert that to yards. 36 inches = 1 yard, so 12 inches = 1/3 yard. Write an equation to find the number of tiles: t x 1/3 = 63. Multiply both sides by 3 to get t = 189.