
Circles and Angles
Geometry questions often involve calculating the area, circumference, and angles of shapes like circles, triangles, and quadrilaterals.
Example 1 (Circle Area)
Find the area of a circle with a radius of 5 cm.
Formula: Area = πr²
Step 1: Use the formula:
Area = π × 5² = 25π
Step 2: Approximate π as 3.14:
Area ≈ 25 × 3.14 = 78.5 cm²
Answer: The area of the circle is approximately 78.5 cm².
Triangles and Trigonometry
SAT Geometry problems often include questions on the properties of triangles and trigonometric ratios. The Pythagorean theorem and sine, cosine, and tangent functions are frequently tested.
Example 2 (Right Triangle)
A right triangle has legs of length 6 and 8. What is the length of the hypotenuse?
Step 1: Use the Pythagorean theorem:
a² + b² = c², where a and b are the legs and c is the hypotenuse.
6² + 8² = c²
36 + 64 = c²
100 = c²
Step 2: Solve for c:
c = √100 = 10
Answer: The hypotenuse is 10.