# Carson Arnold

Geometry teacher | Tutor for 5 years

I'm a Geometry specialist with a passion for unlocking the mysteries of shapes and space. My expertise stems from rigorous study at Ithaca College, where I honed my understanding of geometric principles. With a knack for making complex concepts accessible, I guide students to grasp the beauty and logic of Geometry. Whether it's proofs, theorems, or spatial reasoning, I'm here to illuminate the path to geometric mastery. Let's explore the world of angles and polygons together!

## Questions

What is the perimeter of a rectangle with sides of 12 inches and 18 inches?

Two corners of a triangle have angles of # (5 pi )/ 8 # and # ( pi ) / 4 #. If one side of the triangle has a length of # 14 #, what is the longest possible perimeter of the triangle?

The coordinates of points L and X are 16 and 40, respectively. Point N is the midpoint of LX. What are the coordinates of LN?

A chessboard contains 32 black and 32 white squares. How many squares are along each side of the game board?

What is the perimeter of a triangle with corners at #(3 ,7 )#, #(1 ,1 )#, and #(4 ,3 )#?

A rectangle has an area of 12 square centimeters and a perimeter of 16 centimeters. Which of the following could be its dimensions?

The length of a box is 2 centimeters less than its height. the width of the box is 7 centimeters more than its height. If the box had has a volume of 180 cubic centimeters, what is its surface area?

Triangle A has sides of lengths #12 #, #16 #, and #18 #. Triangle B is similar to triangle A and has a side with a length of #16 #. What are the possible lengths of the other two sides of triangle B?

Point A is at #(5 ,2 )# and point B is at #(2 ,-4 )#. Point A is rotated #(3pi)/2 # clockwise about the origin. What are the new coordinates of point A and by how much has the distance between points A and B changed?

A triangle has corners at #(4, 4 )#, ( 3, -2)#, and #( 2, -1)#. If the triangle is reflected across the x-axis, what will its new centroid be?

The perimeter of a square is 4 times as great as the length of any of its sides. Is the perimeter of a square is proportional to its side length?

What is the equation of the tangent planes to #7x^2-3y^2-z^2+21=0# which passes through the line #7x-6y+9=0#,#z=3#?

The area of a parallelogram is 486 square cm. The sum of its bases is 54 cm. Each slanted side measures 14 cm. What is the height?

A right triangle has sides A, B, and C. Side A is the hypotenuse and side B is also a side of a rectangle. Sides A, C, and the side of the rectangle adjacent to side B have lengths of #7 #, #4 #, and #1 #, respectively. What is the rectangle's area?

Triangle A has sides of lengths #1 3 ,1 4#, and #11 #. Triangle B is similar to triangle A and has a side of length #4 #. What are the possible lengths of the other two sides of triangle B?

Point A is at #(-2 ,-8 )# and point B is at #(-5 ,3 )#. Point A is rotated #(3pi)/2 # clockwise about the origin. What are the new coordinates of point A and by how much has the distance between points A and B changed?

A triangle has two corners with angles of # ( pi ) / 3 # and # ( pi )/ 6 #. If one side of the triangle has a length of #1 #, what is the largest possible area of the triangle?

What is the orthocenter of a triangle with corners at #(9 ,7 )#, #(4 ,4 )#, and (8 ,6 )#?

Two opposite sides of a parallelogram each have a length of #35 #. If one corner of the parallelogram has an angle of #(5 pi)/12 # and the parallelogram's area is #210 #, how long are the other two sides?

A triangle has vertices A, B, and C. Vertex A has an angle of #pi/6 #, vertex B has an angle of #(pi)/12 #, and the triangle's area is #4 #. What is the area of the triangle's incircle?