Geometry Ch 10 - Area Flashcards
Area of Rectangle
A = bh
Area of Parallelogram
A = bh where h is the corresponding height.
Base of a Parallelogram is…
… any of its sides. the corresponding altitude is a segment perpendicular to the line containing that base, drawn from the side opposite the base. The height is the length of an altitude.
Area of a Triangle
A = 1/2(bh)
Base of a Triangle
Any of it’s sides.
Corresponding Height of Triangle
The length of the altitude to the line containing the base of a triangle.
Height of a Trapezoid
The perpendicular distance h between the bases.
Area of a Trapezoid
A = 1/2[h (b1 + b2)]
Area of a Rhombus or a Kite
A = 1/2(d1d2)
Radius of a Regular Polygon
The distance from the center to a vertex.
Apothem of a Regular Polygon
The perpendicular distance from the center to a side.
Area of a Regular Polygon
A = 1/2(ap) where a = the apothem and p = the perimeter.
Perimeters and Areas of Similar Figures
If the similarity ratio of two similar figures is a/b, then
(1) the ratio of their perimeters is a/b and
(2) the ratio of thier areas is a2/b2
Area of a Triangle given SAS
The area of a triangle is one half the product of the lengths of two sides and the sine of the included angle.
Area = 1/2[bc(sin A)
Law of Sines and Cosines
Circle
In a plane, it’s the set of all points equidistant from a given point called the center. You name it by it’s center.
Radius
A segment that has one endpoint at the center and the endpoint on the circle.
Congruent Circles
Have congruent radii.
Diameter
A segment that contains the center of a circle and has both endpoints on the circle.
Central Angle of a Circle
An angle whose vertex is the center of the circle.
Arc
A part of the circumference of a circle or other curve.
Semicircle
One type of an arc that contains half a circle.
Minor Arc
Is smaller than a semicircle.
Major Arc
An arc that is geater than a semicircle.
Adjacent Arcs
Arcs of the same circle that have exactly one point in common.
Arc Addition Postulate
The measure of the arc formed by two adjacent arcs is the sum of the measures of the two arcs.
Circumference of a Circle
C = πd = 2πr
Arc Length
The product of the ratio (measure of the arc)/360 and the circumference of the circle.
Note: It is possible for two arcs of different circles to have the same measure but different lengths, as shown at the left. It is also possible for two arcs of different circles to have the same length but different measures.
Congruent Arcs
Arcs that have the same measure and are in the same circle or in congruent circles.
Area of a Circle
A = πr2
Sector of a circle
A region bounded by an arc of the circle and the two radii to the arc’s endpoints. You name a sector using one arc endpoint, the center of the circle, and the other arc endpoint.
Segment of a Circle
The part of a circle bounded by an arc and the segment joinging its endpoints.
Area of Segment of Circle
The area of the sector minus the area of the triangle formed.
Geometric Probability
Comparing measurements of sets of points.
