# Noah Atkinson

Geometry teacher | Tutor for 8 years

I am a dedicated educator specializing in Geometry, with a background in Mathematics from Washington and Lee University. My passion lies in guiding students through the intricate world of shapes, angles, and proofs, fostering their understanding and appreciation for the subject. With a commitment to clarity and patience, I strive to make geometric concepts accessible and engaging for learners of all levels. Through personalized instruction and effective problem-solving strategies, I aim to empower students to excel in their mathematical journey. Let's unlock the mysteries of Geometry together!

## Questions

Charlene is trying to find the unknown sides of a right triangle with a 30° acute angle, whose hypotenuse measures #12sqrt2#. What is Charlene's error?

A circle has a center that falls on the line #y = 7/6x +1 # and passes through #(1 ,4 )# and #(8 ,5 )#. What is the equation of the circle?

An ellipsoid has radii with lengths of #8 #, #2 #, and #5 #. A portion the size of a hemisphere with a radius of #2 # is removed form the ellipsoid. What is the volume of the remaining ellipsoid?

In an isosceles triangle, each base angle is 30 degrees more than the vertex angle. What are the measures of the three angles?

A solid consists of a cone on top of a cylinder with a radius equal to that of the cone. The height of the cone is #18 # and the height of the cylinder is #36 #. If the volume of the solid is #420 pi#, what is the area of the base of the cylinder?

How are isosceles and scalene triangles the same?

A chord with a length of #24 # runs from #pi/3 # to #pi/2 # radians on a circle. What is the area of the circle?

A triangle has corners at #(2 ,2 )#, #(4 ,-7 )#, and #(3 ,4 )#. If the triangle is dilated by a factor of #5 # about point #(1 ,-9 ), how far will its centroid move?

A parallelogram has sides A, B, C, and D. Sides A and B have a length of #3 # and sides C and D have a length of # 4 #. If the angle between sides A and C is #(7 pi)/18 #, what is the area of the parallelogram?

An ellipsoid has radii with lengths of #5 #, #12 #, and #8 #. A portion the size of a hemisphere with a radius of #7 # is removed form the ellipsoid. What is the remaining volume of the ellipsoid?

If the surface area of a cube is 384 square feet,what is its volume?

A pyramid has a base in the shape of a rhombus and a peak directly above the base's center. The pyramid's height is #7 #, its base has sides of length #5 #, and its base has a corner with an angle of # pi/4 #. What is the pyramid's surface area?

What is the equations of the tangents of the conic #x^2+4xy+3y^2-5x-6y+3=0# which are parallel to the line #x+4y=0#?

A triangle has two corners with angles of # pi / 2 # and # ( pi )/ 8 #. If one side of the triangle has a length of #13 #, what is the largest possible area of the triangle?

A parallelogram has sides with lengths of #24 # and #9 #. If the parallelogram's area is #144 #, what is the length of its longest diagonal?

A line passes through #(4 ,3 )# and #(1 ,4 )#. A second line passes through #(7 ,8 )#. What is one other point that the second line may pass through if it is parallel to the first line?

How do you calculate the area of a triangle without a right angle?

Two rhombuses have sides with lengths of #6 #. If one rhombus has a corner with an angle of #pi/12 # and the other has a corner with an angle of #(7pi)/8 #, what is the difference between the areas of the rhombuses?

Triangle A has an area of #12 # and two sides of lengths #3 # and #8 #. Triangle B is similar to triangle A and has a side of length #9 #. What are the maximum and minimum possible areas of triangle B?

A triangle has vertices A, B, and C. Vertex A has an angle of #pi/8 #, vertex B has an angle of #( pi)/3 #, and the triangle's area is #18 #. What is the area of the triangle's incircle?