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
In triangle ABC, AB = 6, AC = 9, and BC = 10. The angle bisector from A meets BC at D. What is BD?
Answer: 4
BD/DC = 6/9, so BD = 10·6/15 = 4.
Two sides of a triangle have lengths 5 and 7, and the angle between them is 60°. What is the length of the third side?
Answer: √39
c² = 25 + 49 − 2·5·7·(1/2) = 39.
What is the length of the space diagonal of a rectangular box with dimensions 2 × 3 × 6?
Answer: 7
sqrt(4 + 9 + 36) = sqrt(49) = 7.
A lattice polygon has 10 interior lattice points and 8 boundary lattice points. What is its area?
Answer: 13
By Pick's theorem, A = I + B/2 − 1 = 10 + 4 − 1 = 13.
In a triangle with sides 6, 8, and 10, what is the length of the median to the longest side?
Answer: 5
It is a right triangle, so the median to the hypotenuse equals half the hypotenuse.
A circle is inscribed in a square whose diagonal has length 10. What is the area of the circle?
Answer: 25π/2
The side is 5√2, so r = 5√2/2 and r² = 25/2.
What is the area of a triangle with side lengths 7, 8, and 9?
Answer: 12√5
Heron's formula with s = 12 gives sqrt(12·5·4·3) = sqrt(720) = 12√5.
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