Geometry & Measurement Concepts Flashcards

An arc of a circle subtends an angle of 2 radians at the center. If the arc length is 8 cm, what is the area of the sector?

Answer: 16 cm²

Arc length s = rθ → r = 4 cm; sector area = ½r²θ = ½·16·2 = 16 cm².

A regular hexagon has side length 4 cm. What is its area?

Answer: 24√3 cm²

Area of regular hexagon = (3√3/2)s² = (3√3/2)·16 = 24√3 cm².

Two parallel lines are cut by a transversal. One co-interior angle is 3x + 10° and the other is 2x + 20°. Find x.

Answer: 30°

Co-interior (same-side interior) angles sum to 180°: 5x + 30 = 180 → x = 30°.

A cone has base radius 3 cm and slant height 5 cm. What is its total surface area?

Answer: 24π cm²

Total surface area = πrl + πr² = π·3·5 + π·9 = 15π + 9π = 24π cm².

In a circle, a chord of length 16 cm is 6 cm from the center. What is the radius?

Answer: 10 cm

The perpendicular from center bisects the chord; r = √(8²+6²) = √100 = 10 cm.

A square is inscribed in a circle of radius 5 cm. What is the area of the square?

Answer: 50 cm²

The diagonal of the square equals the diameter = 10; side = 10/√2, area = 100/2 = 50 cm².

The angle subtended by a chord at the center is 80°. What is the angle subtended by the same chord at any point on the major arc?

Answer: 40°

The inscribed angle on the major arc is half the central angle: 80°/2 = 40°.