Geometry Problems
44 = 2(3x + 2) + 2(5x + 4) , solve for x
x = 2
height = area / base
= 64 / 14 = 32/7 cm
sin(T) = (32/7) / 8 = 32/56 = 4/7, T = arcsin(4/7) = 34.8o
The distance around a 2 dimensional shape
Perimeter
Tickets numbered 1 to 20 are mixed up and then a ticket is drawn at random. What is the probability that the ticket drawn has a number which is a multiple of 3 or 5?
9/20
any side of a parallelogram
base
A quadrilateral with 4 equal sides and 4 right angles.
Opposite sides are parallel.
Square
Let r be the radius of the semicircle. Area of the semicircle is known; hence
1250Pi = (1/2) Pi r2 (note the 1/2 because of the semicircle)
Solve for r: r = 50
Length of rectangle = 2r = 100 (semicircle inscribed)
Width of rectangle = r = 50 (semicircle inscribed)
Area = 100 * 50 = 5000
The number of unit cubes that can fit inside of the 3D shape.
Volume
A bag contains 2 red, 3 green and 2 blue balls. Two balls are drawn at random. What is the probability that none of the balls drawn is blue?
10/21
the length of the segment perpendicular to the base with endpoints on opposite sides
height
A plane figure that can be folded along a line so the two parts match.
Symmetry
Find the circumference of a circular disk whose area is 100 pi square centimeters.
100 + 4*(1/2)*12*10 = 340 inches squared
The number of square units that cover a shape.
Area of rectangle A = L x W
Area
In a box, there are 8 red, 7 blue and 6 green balls. One ball is picked up randomly. What is the probability that it is neither red nor green?
1/3
A quadrilateral whose opposite sides are parallel and congruent.
parallelogram
A dot that specifies only location; it has no length, width, or depth. We usually represent a it with a dot on paper, but the dot we make has some dimension, while a true point has dimension 0.
point
2 = 152 + 152 = 450 Also BC2 + CD2 = 212 + 32 = 450
The above means that triangle BCD is also a right triangle and the total area of the quadrilateral is the sum of the areas of the two right triangles.
Area of quadrilateral = (1/2)*15*15 + (1/2)*21*3 = 144
A line segment where two faces of a three-dimensional (3D) shape meet.
Edge
What is the probability of getting a sum 9 from two throws of a dice?
1/9
A = ½bh
area of a triangle
Two lines that intersect to form right angles
Perpendicular Lines
The semicircle of area 1250 pi centimeters is inscribed inside a rectangle. The diameter of the semicircle coincides with the length of the rectangle. Find the area of the rectangle.
Volume = (1/3)*100*sqrt(119)
= 363.6 inches cubed (approximated to 4 decimal digits)
The perpindicluar distance from the base of the prism to the top of the prism.
Height
Three unbiased coins are tossed. What is the probability of getting at most two heads?
7/8
A = ½h(b₁ +b₂)
area of a trapezoid
A triangle that has no equal sides. All 3 sides are different lengths.
Scalene Triangle