Perimeter - using coordinate grid/distance formula
What is the formula to calculate the perimeter of a rectangle?
The perimeter is calculated using the formula P=2(l+w)P=2(l+w), where (l) is the length and (w) is the width.
What is the formula for the circumference of a circle with radius r?
C=2πr
What is the area formula for a circle with radius r?
pi(r^2)
How do you calculate the area of a composite figure?
Answer: Divide the figure into simpler shapes, find the area of each, and sum them.
What is the formula for the area of a regular polygon with n sides, each of length s?
A=(1/2)aP
If a triangle has vertices at (1, 2), (4, 6), and (7, 2), how do you calculate its perimeter?
Use the distance formula d=sqaure root of (x2−x1)^2+(y2−y1)^2 to find the lengths of each side and add them together.
If the radius of a circle is 7, what is the circumference?
Answer: C=2π(7)=14π
A circle has a radius of 4. What is its area?
16pi
If a composite figure consists of a rectangle and a semicircle on top with a base of 6, what is the area?
Answer: Area of rectangle plus area of semicircle.
A regular hexagon has a side length of 6. What is the area?
the area of the hexagon is approximately 93.65 square units
A rectangle has vertices at (2,3), (2,8), (6,8), and (6,3). What is the perimeter of this rectangle?
P=2(l+w)=2(4+5)=18
How do you calculate the length of an arc given the central angle in degrees?
Angle/360 X circumference
If the area of a circle is 25π, what is the radius?
5
A composite figure is made up of a rectangle (length 10, width 4) and a triangle (base 4, height 3). What is the total area?
Answer: A=(10×4)+12(4×3)=40+6=46
How do you find the area of a regular polygon if you know the apothem and the perimeter?
Use the formula A=1/2×P×a.
How do you derive the perimeter of a polygon given its vertices on a coordinate grid?
Calculate the distance between each consecutive pair of vertices and sum them.
A circle has a circumference of 31.4. What is its radius?
31.4/2pi
How would you find the area of a circle if you only know the diameter?
Use r=d*2 to find the radius, then use A=πr^2
How would you find the area of a composite figure that includes a parallelogram and a circle?
Answer: Find the area of each shape separately and then add them together.
What is the area of a regular pentagon with a side length of 5?
The area of the regular pentagon is approximately 42.94 square units 42.94
If the distance between points (3,4) and (x,y) is 10 units, what is the equation that represents this relationship?
Answer: (x−3)^2+(y−4)^2=10
If the angle of an arc is 120 degrees and the radius is 5, what is the length of the arc?
10pi/3
In a circle with angle KLM of 78 degrees and a radius of 4, what is the area of the sector KLM
10.89 units squared
If a composite figure includes a rectangle and a triangle with dimensions that create an area of 50 for the rectangle and 12 for the triangle, what is the total area?
Answer: A=50+12=62
A regular nonagon has a side length of 5. What is the area?
The area of the regular nonagon is approximately 173.14 square units.