Area of 2-D Shapes
Find the area of a rectangle with a length of 13 feet and a width of 7 feet
13(7) = 91 feet2
Find the sum of the interior angles of a 9-sided polygon (nonagon)
(9-2)(180) = 1260 degrees
Find the distance between (2,4) and (12,4)
d = 12 - 2 = 10 units
Find the volume of a rectangular prism with dimensions 11 by 12 by 9
V = 1,188 units2
In a right triangle, if the side opposite of angle theta is 6 and the hypotenuse is 10, find the ratio for sin of theta and the value of theta to the nearest whole degree.
sin-1(6/10) = theta = 37
Find the area of a triangle with a base of 18 units and sides of 41 units
A = 360 units2
Determine the area of a regular hexagon with a perimeter of 120 inches
Each side is 20 inches
A = 1,039.23 inches2
A ladder is 25 feet long and leans against a wall that is 24 feet high. How far is the base from the wall?
d = (sqrt(252-242) = 7 feet
Find the volume of a cylinder with a radius of 8mm and a height of 17.5mm. In exact form!
V = 1120pi mm3
A 15-foot ladder leans against a building. If the ladder makes a 70 degree angle with the ground, how high up the wall does the ladder reach?
sin(70) = h/15
h= 15(sin(70)) = 14.095 ft
Determine the area of a parallelogram with sides of 12 mi and 8 mi and an included angle of 60 degrees
A = 12(8)(sin(60)) = 83.138 mi2
Find the measure of one interior angle of a regular 10-sided polygon.
((10-2)*180)/10 = 144
Find the perimeter of a triangle with vertices A (2,4), B (5,1), and C( -1,-3)
Answer = 19.070 units
Find the total surface area of a triangular prism with a height of 11 and base edges 17, 17, 16
SA = 2(120)+(17+17+16)(11) = 790 units2
In an equilateral triangle with sides 16, find the altitude (height) using trig.
h = 16(sin(60)) = 8sqrt(3) = 13.856 units
Find the area of the shaded region in a 13 ft by 7 ft rectangle containing a 7 ft by 3 ft inner rectangle centered with margins.
A= (13(7))-(7(3)) = 91 - 21 = 70 feet2
Determine the area of a regular octagon with a perimeter of 400 feet.
Answer= 12,071.068 feet2
Find the diagonal of a rectangular solid with dimensions 8, 12, and 9.
d = (sqrt(82+122+92) = (sqrt(289)) = 17 units
Find the volume of a regular pentagonal prism with h = 10 and Lateral Surface Area of 1000
S = 20
V = (base area)(10) = 6,881.91 units3
Find the measures of the interior angles of an isosceles triangle with sides 17, 17, 16.
cos-1(8/17) = A
A = 61.928
Angles 61.928, 61.928, 56.145
Determine the area of an isosceles trapezoid with bases 8 and 12 and base angle 30 degrees
h = 2(tan(30)) = 1.155
A = (8+12)/2 * (1.155) = 11.547 units2
Find the area of a regular pentagon with a perimeter of 20 units.
Answer = 27.528 units2
Determine the distance from (0,0) to a point reached by travelling 3 km North and 4 km west.
sqrt(32+42) = 5 km
If all sides of a triangular prism with V = 20 in3 are tripled, what is the new volume?
New V = 20(33) = 540 inches3
A visitor at a cabin 6 mi west of a point on a shore wants to reach an island 2 mi north of that point. If they run at 8 mph and swim at 3 mph, find the optimal distance to run to minimize time.
Distance = 5.191 along the sand before swimming