Chapter 17: Geometry Flashcards
What is the sum of the interior angles of a triangle?
180°
What is the sum of the exterior angles of a triangle?
360°
What is the formula for the area of a right triangle?
Area = 1/2 base x height
What is the triangle inequality theorem?
In any triangle, the sum of the lengths of any two sides is greater than the length of the third side
What is the ratio of the lengths of the sides of a 45-45-90 right triangle?
x : x : x√2
What is the ratio of the lenghts of the sides of a 30-60-90 right triangle?
x : x√3 : 2x
What is the formula for the area of an equilateral triangle?
A = (s2√3)/4
What is the formula for the area of a parallelogram?
base x height
What is the formula for the diagonal of a rectangle?
√(L2 +W2)
(This is also essentially the pythagorean theorem)
What is the formula for the area of a trapezoid?
((base1 + base2) x height)/2
What is the formula for the sum of the interior angles of a regular polygon?
(n-2) x 180, where n = the number of sides of the polygon
What is the sum of the interior angles of a hexagon?
720°
What is the formula for the area of a regular hexagon?
((3√3)/2)s2 where s = the length of one side of the hexagon
What is the sum of the exterior angles of a polygon?
360°
What is the formula for the circumference of a circle?
π2r or πd, where r = the radius and d = the diameter
What is the formula for the area of a circle?
A = πr2
What is the three-part ratio for any circle?
central angle/360 = arc length/circumference = area of sector/area of circle
What is the degree measure of an inscribed angle of a circle, compared to the degree measure of the arc it intercepts?
one half
What is the formula for the shaded regions of a figure?
Area of the figure - the area of the unshaded regions
What is the formula for the area of a circular ring?
Area = π(R22 - R12)
What is the formula for the volume of a cube?
side3
What is the formula for the volume of a rectangular solid?
lengh x width x height
What is the formula for the length of a diagonal drawn within the interior of a rectangular solid?
d = l2 + w2 + h2
What is the formula for the surface area of a cube?
6s2, where s = the length of one side
What is the formula for the surface area of a rectangular solid?
2(LW) + 2(LH) + 2(WH)
What is the formula for the volume of a cylinder?
πr2h, aka circumference x height
What is the formula for the surface area of a cylinder?
2πr2 + 2πrh
What is the formula for time when filling a container?
Time = volume / rate of fill
