SAT · Geometry and Trigonometry
Find the area of rectangles, squares, triangles, and circles, and use V = Bh to find the area of a base.
SAT formula sheet
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Search each Question ID at satsuitequestionbank.collegeboard.org under Geometry and Trigonometry, skill Area and volume, for the full stem, choices, and rationale.
| Question ID | Difficulty | Topic Focus |
|---|---|---|
| 0e40dfb0 ⭐ | Easy | Area of rectangle |
| 165c30c4 ⭐ | Easy | Area of rectangle |
| 3453aafc ⭐ | Easy | Area of rectangle |
| 4420e500 ⭐ | Easy | Area of rectangle |
| 4efea6a3 ⭐ | Easy | Given area of rectangle, find length |
| 5252e606 ⭐ | Easy | Area of square |
| 575f1e12 ⭐ | Easy | Area of rectangle |
| 59cb654c ⭐ | Easy | Given area of square, find length |
| 689abc2a ⭐ | Easy | Area of rectangle − area of square |
| 93f48423 ⭐ | Easy | Area of rectangle |
| 9d2e7037 ⭐ | Easy | Area of rectangle |
| a490003a ⭐⭐ | Easy | Area of rectangle where the length is # more than the width |
| c88183f7 ⭐ | Easy | Perimeter of rectangle |
| d2047497 ⭐ | Easy | Area of rectangle |
| f39f88b7 ⭐ | Easy | Area of a triangle |
| f60bb551 ⭐ | Easy | Find width of rectangle given area and length |
| 08b7a3f5 ⭐⭐ | Medium | Given volume of a triangular prism as Bh, the volume and height of the prism, find the area. |
| 096c7ef5 ⭐⭐⭐ | Medium | Find the diameter of a circle given three points on a graph. |
| 468613c0 ⭐ | Medium | Area of a triangle |
| 5afbdc8e ⭐⭐⭐ | Medium | Find the side length of a square given the area. Need more help with this idea? |
| 6ae1360d ⭐⭐ | Medium | Area of a circle |
| 96467fea ⭐⭐ | Medium | Area of two circles, where students are given the area of one circle in terms of π and have to calculate the area of the other circle |
| 98c12e38 ⭐⭐ | Medium | Area of two circles, where students are given the area of one circle in terms of π and have to calculate the area of the other circle |
| 9c0a0eca ⭐ | Medium | Area of a triangle |
| a4ed5285 ⭐ | Medium | Area of a triangle |
| aef4fd8a ⭐⭐ | Medium | Expression for area of a square |
| c4e5e23c ⭐⭐⭐ | Medium | Find the area of a square, given the area of another square and how the length is related to the other square. |
| e86f0651 ⭐⭐ | Medium | Area of a circle in terms of π given radius |
| 099526fc ⭐⭐⭐⭐ | Hard | Given area of a triangle and a side length, find the height. Contains radicals. This is a great problem!! |
| 306264ab ⭐⭐⭐⭐ | Hard | Given three side lengths of a right triangle, find the area. Remember, the hypotenuse is the longest side. This is a great problem! |
| eb70d2d0 ⭐⭐⭐⭐⭐ | Hard | Area of non-right triangle, given three points, inscribe the triangle into a rectangle |
Tip: Search these exact Question IDs in the College Board SAT Suite Question Bank, Geometry and Trigonometry, skill Area and volume for full questions and rationales.
Area and perimeter from the formula sheet.
A rectangle is 11 cm long and 6 cm wide. What is the area?
A = ℓw
A = 11 × 6
A = 66
Answer: 66 square centimeters
A rectangle is 14 feet long and 5 feet wide. What is the perimeter?
P = 2ℓ + 2w
P = 2(14) + 2(5)
P = 28 + 10
P = 38
Answer: 38 feet
A square has a side length of 7 inches. What is the area?
A = s²
A = 7²
A = 49
Answer: 49 square inches
A triangle has a base of 14 meters and a height of 6 meters. What is the area?
A = 12bh
A = 12 × 14 × 6
A = 42
Answer: 42 square meters
A circle has a radius of 5. What is the area? Leave the answer in terms of π.
A = πr²
A = π(5)²
A = 25π
Answer: 25π
A rectangle has an area of 54 and a length of 9. What is the width?
A = ℓw
54 = 9 × w
w = 6
Answer: 6
A right triangle has side lengths 20, 21, and 29. Find the area.
The longest side is the hypotenuse.
20² = 400
21² = 441
29² = 841
400 + 441 = 841, so 29 is the hypotenuse. The legs are 20 and 21.
A = 12bh
A = 12 × 20 × 21
A = 210
Answer: 210
A triangle has area 56 and a base of 14. The height is a whole number. Find the height.
A = 12bh
56 = 12 × 14 × h
56 = 7h
h = 8
Answer: 8
The volume and the height are given. Find the area of the base. Each solid is different.
A right rectangular prism has a volume of 192 cubic inches. The height is 8 inches. What is the area of the base?
V = Bh
192 = B × 8
B = 24
Answer: 24 square inches
A right triangular prism has a volume of 150 cubic centimeters. The height is 10 centimeters. What is the area of the base?
V = Bh
150 = B × 10
B = 15
Answer: 15 square centimeters
A right cylinder has a volume of 63π cubic feet. The height is 7 feet. What is the area of the base?
V = Bh
63π = B × 7
B = 9π
Answer: 9π square feet
The diameter is the horizontal or vertical side. Count it on the grid. Give the answer in terms of π and as a decimal to two places.
Triangle ABC is inscribed in a circle. The vertices are A(1, 2), B(9, 2), and C(5, 6). Find the circumference of the circle.
AB is horizontal. Count that side. It is a diameter.
The diameter is 8.
The radius is half the diameter.
r = 82
r = 4
C = 2πr
C = 2π(4)
C = 8π
8π ≈ 25.13
Answer: 8π or 25.13
Triangle ABC is inscribed in a circle. The vertices are A(2, 1), B(2, 7), and C(5, 4). Find the area of the circle.
AB is vertical. Count that side. It is a diameter.
The diameter is 6.
The radius is half the diameter.
r = 62
r = 3
A = πr²
A = π(3)²
A = 9π
9π ≈ 28.27
Answer: 9π or 28.27
Triangle ABC is inscribed in a circle. The vertices are A(1, 4), B(11, 4), and C(6, 9). Find the circumference of the circle.
AB is horizontal. Count that side. It is a diameter.
The diameter is 10.
The radius is half the diameter.
r = 102
r = 5
C = 2πr
C = 2π(5)
C = 10π
10π ≈ 31.42
Answer: 10π or 31.42
The side lengths are simplified radicals. Decide which side is the hypotenuse before you use the area formula.
A right triangle has side lengths 2, 2, and 4. Find the area.
Square each side. The greatest square belongs to the hypotenuse.
(2)2 = 2² × 7
= 4 × 7
= 28
(2)2 = 2² × 3
= 4 × 3
= 12
4² = 16
12 + 16 = 28, so 2 is the hypotenuse.
The legs are 2 and 4.
A = 12bh
A = 12 × 2 × 4
A = 4
Answer: 4
A right triangle has side lengths 6, 3, and 3. Find the area.
Square each side. The greatest square belongs to the hypotenuse.
6² = 36
(3)2 = 3² × 6
= 9 × 6
= 54
(3)2 = 3² × 2
= 9 × 2
= 18
36 + 18 = 54, so 3 is the hypotenuse.
The legs are 6 and 3.
A = 12bh
A = 12 × 6 × 3
A = 9
Answer: 9
A right triangle has side lengths , 2, and 3. Find the area.
Square each side. The greatest square belongs to the hypotenuse.
()2 = 65
(2)2 = 2² × 5
= 4 × 5
= 20
(3)2 = 3² × 5
= 9 × 5
= 45
20 + 45 = 65, so is the hypotenuse.
The legs are 2 and 3.
A = 12bh
A = 12 × 2 × 3
A = 3 × 5
A = 15
Answer: 15
A right triangle has side lengths 3, , and 2. Find the area.
Square each side. The greatest square belongs to the hypotenuse.
(3)2 = 3² × 2
= 9 × 2
= 18
()2 = 26
(2)2 = 2² × 2
= 4 × 2
= 8
18 + 8 = 26, so is the hypotenuse.
The legs are 3 and 2.
A = 12bh
A = 12 × 3 × 2
A = 3 × 2
A = 6
Answer: 6
A right triangle has side lengths 2, 5, and 3. Find the area.
Square each side. The greatest square belongs to the hypotenuse.
(2)2 = 2² × 10
= 4 × 10
= 40
(5)2 = 5² × 2
= 25 × 2
= 50
(3)2 = 3² × 10
= 9 × 10
= 90
40 + 50 = 90, so 3 is the hypotenuse.
The legs are 2 and 5.
A = 12bh
A = 12 × 2 × 5
A = 5
= ×
= 2
A = 5 × 2
A = 10
Answer: 10
Inscribe the triangle in a rectangle. Subtract the three right triangles in the corners.
A triangle has vertices A(2, 1), B(8, 3), and C(5, 7). Find the area.
Draw a rectangle around the triangle. Each side of the rectangle passes through the highest, lowest, leftmost, or rightmost vertex.
The width is 8 − 2 = 6.
The height is 7 − 1 = 6.
A = ℓw
A = 6 × 6
A = 36
Three right triangles fill the corners. Find each area.
Right angle at (8, 1). The legs are 6 and 2.
A = 12bh
A = 12 × 6 × 2
A = 6
Right angle at (8, 7). The legs are 3 and 4.
A = 12bh
A = 12 × 3 × 4
A = 6
Right angle at (2, 7). The legs are 3 and 6.
A = 12bh
A = 12 × 3 × 6
A = 9
Area of the triangle = area of the rectangle − the three right triangles.
36 − 6 − 6 − 9 = 15
Answer: 15
A triangle has vertices A(1, 4), B(7, 2), and C(3, 8). Find the area.
Draw a rectangle around the triangle. Each side of the rectangle passes through the highest, lowest, leftmost, or rightmost vertex.
The width is 7 − 1 = 6.
The height is 8 − 2 = 6.
A = ℓw
A = 6 × 6
A = 36
Three right triangles fill the corners. Find each area.
Right angle at (1, 2). The legs are 6 and 2.
A = 12bh
A = 12 × 6 × 2
A = 6
Right angle at (7, 8). The legs are 4 and 6.
A = 12bh
A = 12 × 4 × 6
A = 12
Right angle at (1, 8). The legs are 2 and 4.
A = 12bh
A = 12 × 2 × 4
A = 4
Area of the triangle = area of the rectangle − the three right triangles.
36 − 6 − 12 − 4 = 14
Answer: 14
A triangle has vertices A(2, 7), B(9, 5), and C(4, 1). Find the area.
Draw a rectangle around the triangle. Each side of the rectangle passes through the highest, lowest, leftmost, or rightmost vertex.
The width is 9 − 2 = 7.
The height is 7 − 1 = 6.
A = ℓw
A = 7 × 6
A = 42
Three right triangles fill the corners. Find each area.
Right angle at (9, 7). The legs are 7 and 2.
A = 12bh
A = 12 × 7 × 2
A = 7
Right angle at (9, 1). The legs are 5 and 4.
A = 12bh
A = 12 × 5 × 4
A = 10
Right angle at (2, 1). The legs are 2 and 6.
A = 12bh
A = 12 × 2 × 6
A = 6
Area of the triangle = area of the rectangle − the three right triangles.
42 − 7 − 10 − 6 = 19
Answer: 19
A triangle has vertices A(9, 8), B(1, 5), and C(5, 2). Find the area.
Draw a rectangle around the triangle. Each side of the rectangle passes through the highest, lowest, leftmost, or rightmost vertex.
The width is 9 − 1 = 8.
The height is 8 − 2 = 6.
A = ℓw
A = 8 × 6
A = 48
Three right triangles fill the corners. Find each area.
Right angle at (1, 8). The legs are 8 and 3.
A = 12bh
A = 12 × 8 × 3
A = 12
Right angle at (1, 2). The legs are 4 and 3.
A = 12bh
A = 12 × 4 × 3
A = 6
Right angle at (9, 2). The legs are 4 and 6.
A = 12bh
A = 12 × 4 × 6
A = 12
Area of the triangle = area of the rectangle − the three right triangles.
48 − 12 − 6 − 12 = 18
Answer: 18
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