Abeka Plane Geometry Test 11

Complementary

A central angle of a regular polygon and a vertex angle of the polygon are never ____________

True

A circle can be circumscribed about any regular polygon.

10 sq in K(sect)/K = θ/360° K(sect) = K*θ/360° K(sect) = (80*45°)/360° K(sect) = 10

A circle has an area of 80 square inches. Find the area of a sector who central angle contains 45°.

True

A radius of a regular polygon bisects the vertex angle of the polygon to which it is drawn.

5as

A regular decagon has a side who length is represented by s and an apothem those length is represented by a. The area of the decagon is represented by ___________

True

A regular polygon is equiangular.

False

An apothem of the regular polygon is the radius of the circumscribed circle.

50 in. S/C = θ/360° C = S*360°/θ C = (10*360°)/72° C = 50

An arc of a circle contains 72° and is 10 inches long. Find the circumference of the circle.

False

An equiangular polygon inscribed in a circle is regular.

False (A rhombus is only regular when it is a square)

An equilateral polygon is a regular polygon.

Is constant

As the length of the radius of a circle increases, the ratio of the circumference to the diameter of the circle __________

False Ex: θ = 360°/n → as n goes up, 360°/n goes down

As the number of sides of a regular polygon increases, the number of degrees in the central angles of those polygons increases also.

False

As the number of sides of a regular polygon inscribed in a circle increases, the length of the apothem of the polygon decreases.

20° θ=360°/n = 360°/18 = 20°

Find the measure of the central angle of an 18-sided regular polygon.

12 sides angle at center = 180°-150° = 30° θ = 360°/n 30° = 360°/n n = 360°/30° n = 12

Find the number of sides a regular polygon will have if each vertex angle measures 150°.

False The arc must be equal

If a circle is divided intro three or more arcs, the chords of these arces form a regular polygon.

4 in. - the apothem is the short leg; the radius is the hypotenuse of a 30-60-90 triangle. The leg is half of the radius.

If an equilateral triangle is inscribed in a circle whose radius is 8 inches long, find the length of its apothem.

16 → π(4r)² or the area would work to 16 times (4²=16)

If the length of the radius of a circle is multiplied by 4, then the area of the circle is multiplied by _______

False

If the length of the radius of a circle is multiplied by a positive number s, the circumference of the circle is multiplied by s².

True Ex: K = πr² = π*2² = 4π, C = 2πr = 2*π*2 = 4π

If the radius of a circle is 2 inches, the number of square inches in the area of the circle is the same number as the number of number of inches in the circumference.

16 in. - the radii are to each other as the square root of the areas. The ratio of the areas is 1:4, so the ratio of the radii is 1:2. For example: 8:16.

If the radius of a circle is 8 inches, find the radius of a circle who area is four times as large.

64 sq in A₁/A₂ = (s₁)²/(s₂)² A₁/36 = (8)²/(6)² A₁ = (36*8²)/6² A₁ = 64

If two similar polygons have corresponding sides that measure 6 and 8 inches respectively, and the area of the smaller one is 36 square inches, what would be the area of the larger polygon?

4 to 25 K₁/K₂ = (r₁)²/(r₂)² = (4)²/(10)² = 16/100 = 4/25

In question number 26, what would be the ratio of their areas?

50π - 96 sq in ∠C=90° c²=a+b → 12²+16²=400 c=20, so r=10 semicircle = K/2 = πr²/2 = (π*10²)/2 = 50π T(abc) = ½bh = ½*12*16 = 96 shaded = semicircle - T(abc) = 50π - 96 sq in

In the semicircle given, the length of chord AC is 16 inches, and the length of chord BC is 12 inches. Find the area of the shaded region. Leave your answer in terms of pi if applicable.

2 to 5 C₁/C₂ = r₁/r₂ = 4/10 = 2/5

Question #26: If two circles have radii of 4 inches and 10 inches respectively, them what would be the ratio of their circumferences?

True

Regular polygons of the same number of sides are similar.

¼πd²

The area of a circle with a diameter who length is represented by d is represented by ________

False

The area of a regular polygon is equal to the product of its perimeter and its apothem.

False K/K' = (r)²/(r')²

The ratio of the areas of two circles that are not equal is the same as the ratio of lengths of the radii of the two circles.

True

The ratio of the circumference of a circle to its diameter is constant.