# Caroline Aucoin

Geometry teacher | Verified Expert

I hold a degree in Geometry from Montclair State University. With a passion for unlocking the mysteries of shapes and spaces, I guide students through the intricacies of geometric concepts. My teaching style emphasizes clarity and practical application, empowering learners to excel in problem-solving and critical thinking. Drawing on my academic background and real-world experience, I foster a supportive learning environment where curiosity thrives. Together, we'll explore the fascinating world of geometry and uncover its relevance in everyday life. Let's embark on this journey of discovery together.

## Questions

A triangle has corners at #(3 ,8 )#, #(5 ,9 )#, and #(8 ,2 )#. What is the area of the triangle's circumscribed circle?

How do you find the hypotenuse if the length of the legs of a right triangle are 30 ft and 40 ft?

What is the surface area of a 11 cm high pyramid whose base is an equilateral triangle with a 62 cm perimeter? Show work.

Two corners of an isosceles triangle are at #(5 ,6 )# and #(4 ,8 )#. If the triangle's area is #36 #, what are the lengths of the triangle's sides?

What is the perimeter of a triangle with corners at #(1 ,5 )#, #(8 ,3 )#, and #(4 ,1 )#?

A triangle has two corners with angles of # pi / 12 # and # pi / 8 #. If one side of the triangle has a length of #6 #, what is the largest possible area of the triangle?

Two opposite sides of a parallelogram each have a length of #2 #. If one corner of the parallelogram has an angle of #(2 pi)/3 # and the parallelogram's area is #15 #, how long are the other two sides?

A triangle has corners at points A, B, and C. Side AB has a length of #18 #. The distance between the intersection of point A's angle bisector with side BC and point B is #7 #. If side AC has a length of #14 #, what is the length of side BC?

Two opposite sides of a parallelogram each have a length of #12 #. If one corner of the parallelogram has an angle of #(3pi)/8 # and the parallelogram's area is #24 #, how long are the other two sides?

How can an isosceles triangle have a right angle?

A triangle has corners A, B, and C located at #(2 ,5 )#, #(7 ,4 )#, and #(3 , 5 )#, respectively. What are the endpoints and length of the altitude going through corner C?

The base of a triangular pyramid is a triangle with corners at #(1 ,3 )#, #(2 ,2 )#, and #(8 ,5 )#. If the pyramid has a height of #7 #, what is the pyramid's volume?

How do you write an equation of a circle with center at (5,10), r=7?

Two corners of an isosceles triangle are at #(5 ,2 )# and #(2 ,1 )#. If the triangle's area is #6 #, what are the lengths of the triangle's sides?

Two corners of an isosceles triangle are at #(8 ,1 )# and #(1 ,4 )#. If the triangle's area is #15 #, what are the lengths of the triangle's sides?

A cone has a height of #14 cm# and its base has a radius of #7 cm#. If the cone is horizontally cut into two segments #2 cm# from the base, what would the surface area of the bottom segment be?

What is the centroid of a triangle with corners at #(5, 1)#, #(4, 9)#, and #(7,2)#?

A triangle has corners at #(1 ,9 )#, #(7 ,8 )#, and #(4 ,5 )#. How far is the triangle's centroid from the origin?

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 #4 #, #1 #, and #5 #, respectively. What is the rectangle's area?

An ellipsoid has radii with lengths of #8 #, #9 #, and #2 #. A portion the size of a hemisphere with a radius of #5 # is removed form the ellipsoid. What is the volume of the remaining ellipsoid?