# Avery Allen

Geometry teacher | Experienced educator in USA

I'm a passionate Geometry tutor with a degree from Mercyhurst University. My dedication to illuminating the intricacies of shapes and space stems from my profound understanding of mathematical concepts. With a knack for simplifying complex theorems, I empower students to conquer geometric challenges with confidence. Whether it's unraveling the mysteries of angles or navigating the realm of proofs, I'm committed to fostering a deep appreciation for Geometry and igniting a lifelong love for mathematical exploration. Let's embark on a journey of geometric discovery together!

## Questions

A circle has a center at #(7 ,6 )# and passes through #(2 ,1 )#. What is the length of an arc covering #pi/12# radians on the circle?

An isosceles triangle has sides A, B, and C, such that sides A and B have the same length. Side C has a length of #8 # and the triangle has an area of #16 #. What are the lengths of sides A and B?

What is the sum of the measures of the interior angles of an octagon?

A rectangular parking lot has a length that is 7 yards than the width. The area of the parking lot is 120 square greater yards. What is the length and the width?

How do I prove that if a quadrilateral has consecutive angles that are supplementary, then it is a parallelogram?

Triangle A has sides of lengths #7 ,4 #, and #5 #. Triangle B is similar to triangle A and has a side of length #3 #. What are the possible lengths of the other two sides of triangle B?

A triangle has corners A, B, and C located at #(7 ,6 )#, #(8 ,3 )#, and #(2 ,1 )#, respectively. What are the endpoints and length of the altitude going through corner C?

A triangle has corners at #(6 ,4 )#, #(6 ,5 )#, and #(3 ,3 )#. What is the area of the triangle's circumscribed circle?

Cups A and B are cone shaped and have heights of #35 cm# and #23 cm# and openings with radii of #14 cm# and #9 cm#, respectively. If cup B is full and its contents are poured into cup A, will cup A overflow? If not how high will cup A be filled?

A parallelogram has sides with lengths of #14 # and #8 #. If the parallelogram's area is #16 #, what is the length of its longest diagonal?

What are some proofs that could be used to prove that a given rhombus is a square?

An ellipsoid has radii with lengths of #6 #, #9 #, and #4 #. A portion the size of a hemisphere with a radius of #5 # is removed form the ellipsoid. What is the remaining volume of the ellipsoid?

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?

A triangle has corners at #(-5 ,6 )#, #(2 ,-3 )#, and #(8 ,9 )#. If the triangle is dilated by a factor of #5 # about point #(-3 ,6 ), how far will its centroid move?

And I saucily‘s right triangles legs are 10 square root of 8 feet long. What is the length of the hypotenuse?

Circle A has a center at #(9 ,-2 )# and a radius of #1 #. Circle B has a center at #(1 ,3 )# and a radius of #3 #. Do the circles overlap? If not, what is the smallest distance between them?

A rectangular room measures 12ft by 15ft. the entire room is to be covered with rectangular tiles that measures 5in by 4in. if the tiles are sold for &2.50 a dozen what will it cost to tile the room?

Two corners of an isosceles triangle are at #(4 ,8 )# and #(5 ,7 )#. If the triangle's area is #5 #, what are the lengths of the triangle's sides?

Gena is working on her math project. She has trimmed the sides of a square cardboard by 7 decimeters. The area of the cardboard then has decreased by 81 square decimeters. What was the original length of a side of the cardboard?

A triangle has corners at points A, B, and C. Side AB has a length of #48 #. The distance between the intersection of point A's angle bisector with side BC and point B is #8 #. If side AC has a length of #42 #, what is the length of side BC?