Geometry & Measurement Flashcards
7 cards from real AMC 12 practice questions. Tap to flip, then mark Knew It or Still Learning — missed cards come back until you master them.
Read the first 7 Geometry & Measurement flashcards as text
What is the area of a triangle with side lengths 13, 14, and 15?
Answer: 84
Heron's formula with s = 21 gives sqrt(21·8·7·6) = sqrt(7056) = 84.
What is the circumradius of a triangle with side lengths 13, 14, and 15?
Answer: 65/8
R = abc/(4K) = 2730/(4·84) = 65/8.
What is the inradius of a right triangle with legs 3 and 4?
Answer: 1
r = Area/s = 6/6 = 1.
What is the area of a regular hexagon with side length 2?
Answer: 6√3
A regular hexagon is six equilateral triangles of area √3 each, so the total is 6√3.
A sphere is inscribed in a cube with edge length 6. What is the volume of the sphere?
Answer: 36π
The radius is 3, so V = (4/3)π(27) = 36π.
What is the distance from the point (1, 2) to the line 3x + 4y − 1 = 0?
Answer: 2
|3 + 8 − 1|/sqrt(9 + 16) = 10/5 = 2.
How many diagonals does a convex decagon have?
Answer: 35
n(n − 3)/2 = 10·7/2 = 35.
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