SAT Geometry and Trigonometry practice questions
Angles, triangles, circles, volume and right-triangle trigonometry, usually with a diagram to decode.
38 free questions, each with a full worked solution and an explanation of what each wrong answer means.
Practise this domain adaptively →Easy (7)
- Triangle angle sum
Two angles of a triangle measure 40° and 75°. What is the measure of the third angle? - Area of a triangle
A triangle has a base of 10 and a height of 6. What is its area? - Special right triangles (30-60-90)
In a 30°-60°-90° right triangle, the shorter leg (opposite the 30° angle) has length 6. What is the length of the hypote… - Perimeter of a rectangle
A rectangle has a length of 8 and a width of 3. What is its perimeter? - Volume of a rectangular prism
A closed rectangular box has a length of 5 inches, a width of 4 inches, and a height of 3 inches. What is the volume of … - Equation of a circle in the xy-plane
In the xy-plane, a circle has center (2, −5) and radius 3. Which equation represents this circle? - Relating area and perimeter of a square
A square has an area of 36 square centimeters. What is the perimeter, in centimeters, of the square?
Easy–Medium (7)
- Circles: area and circumference
A circle has a radius of 6. What is its area? (Use A = πr².) - Pythagorean theorem
A right triangle has legs of length 6 and 8. What is the length of the hypotenuse? - Circumference of a circle
A circle has a radius of 5. What is its circumference? (Use C = 2πr.) - Midpoint in the coordinate plane
What is the midpoint of the segment joining the points (2, 3) and (8, 11)? - Exterior angle theorem / angles in a triangle
What is the measure, in degrees, of angle B? - Area of a trapezoid
What is the area, in square centimeters, of the trapezoid? - Right triangle trigonometry (cosine ratio)
What is the value of cos A?
Medium (9)
- Special right triangles (45-45-90)
In a 45°-45°-90° right triangle, each leg has length 5. What is the length of the hypotenuse? - Volume of a cylinder
A cylinder has a radius of 3 and a height of 10. What is its volume? (Use V = πr²h.) - Trigonometric ratios (SOH-CAH-TOA)
In a right triangle, the side opposite angle θ has length 3 and the hypotenuse has length 5. What is sin θ? - Similar triangles
Two triangles are similar with a ratio of 2 to 3. A side of the smaller triangle measures 8. What is the length of the c… - Distance in the coordinate plane
What is the distance between the points (1, 2) and (4, 6) in the coordinate plane? - Area of a sector
A circle has a radius of 6. What is the area of a sector with a central angle of 60°? - Volume of a sphere
A sphere has a radius of 3. What is its volume? (Use V = (4/3)πr³.) - Slope in the coordinate plane
What is the slope of the line passing through the points (-2, 1) and (4, 10)? - Trigonometric ratios (tangent)
In a right triangle, the side opposite angle θ has length 8 and the side adjacent to angle θ has length 15. What is the …
Hard (7)
- Right triangles and the Pythagorean theorem
In a right triangle, one leg is 5 and the hypotenuse is 13. What is the length of the other leg? - Arc length
A circle has a radius of 4. What is the length of an arc that subtends a central angle of 90°? - Equation of a circle
A circle is defined by the equation (x − 3)² + (y + 2)² = 25. What is the radius of the circle? - Converting degrees to radians
What is 135° expressed in radians? - Circles in the coordinate plane: completing the square and tangent lines
What is the length of segment PT? - Arc length and sector area with radian measure
What is the measure, in degrees, of the central angle of this sector? - Right triangle trigonometry with similarity scaling
What is the area, in square units, of triangle ABC?
Very hard (8)
- Angles formed by parallel lines
Two parallel lines are cut by a transversal. One of the eight angles measures 47°. Which of the following is NOT a possi… - Complementary angle trig identity (sin/cos)
In a right triangle, angles A and B are the two acute angles, so A + B = 90°. If sin A = 0.6, what is the value of cos B… - Area of a regular polygon (hexagon)
A regular hexagon has a side length of 4. What is its area? (A regular hexagon of side s has area (3√3/2)s².) - Volume of a cone
A cone has a radius of 6 and a height of 10. What is its volume? (Use V = (1/3)πr²h.) - Circles in the coordinate plane: chord length from a line–circle intersection
In the xy-plane, the graph of x² + y² − 12x − 4y + 15 = 0 is a circle. The line 3x − 4y = 25 intersects this circle at t… - Similar triangles formed by the altitude to the hypotenuse of a right triangle
What is the perimeter of triangle ABC? - Volumes of similar solids (partially filled cone)
What is the volume, in cubic inches, of the water in the cup? - Tangent lines, central angles, and arc length
What is the length of minor arc AB?
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