# 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 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 #5 #, #4 #, and #12 #, respectively. What is the rectangle's area?

An object is made of a prism with a spherical cap on its square shaped top. The cap's base has a diameter equal to the lengths of the top. The prism's height is #6 #, the cap's height is #4 #, and the cap's radius is #6 #. What is the object's volume?

A plate has its dimensions #4.234m#, #1.005m# and thickness is #2.01# #cm.# What is its surface area and volume?

A line segment has endpoints at #(9 ,3 )# and #(5 ,9 )#. The line segment is dilated by a factor of #3 # around #(4 ,4 )#. What are the new endpoints and length of the line segment?

In the following figure what is #/_GDH#, interior or exterior angle?

What is the difference in volume between a baseball with a diameter of 1.75 in and a soccer ball with a diameter of 9.50 in?

What is the area of a circle whose radius is (-3x+10) centimeters?

Triangle A has an area of #5 # and two sides of lengths #6 # and #3 #. Triangle B is similar to triangle A and has a side with a length of #9 #. What are the maximum and minimum possible areas of triangle B?

A circle has a center that falls on the line #y = 2/7x +3 # and passes through # ( 2 ,8 )# and #(3 ,5 )#. What is the equation of the circle?

Cups A and B are cone shaped and have heights of #32 cm# and #14 cm# and openings with radii of #15 cm# and #12 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?

What is the orthocenter of a triangle with corners at #(3 ,6 )#, #(3 ,2 )#, and (5 ,7 )#?

I need an expression in simplest form for the perimeter of a triangle, left side of the triangle says 2x bottom line says 4x-2 and right side says 2x+3?

A pyramid has a parallelogram shaped base and a peak directly above its center. Its base's sides have lengths of #3 # and #2 # and the pyramid's height is #6 #. If one of the base's corners has an angle of #pi/4 #, what is the pyramid's surface area?

What is the perimeter of a triangle with corners at #(6 ,4 )#, #(8 ,2 )#, and #(4 ,7 )#?

A gymnast performs a tumbling run along the diagonal of a square mat with sides that are 35 feet long. What distance does the gymnast tumble?

The ratio of two sides of a parallelogram is 3:4. If its perimeter is 56cm, what are the lengths of the sides?

#a# and #b# are the legs of a right triangle. #c# is the hypotenuse. If #c=13, b=2a#, what is #a# and #b#?

An ellipsoid has radii with lengths of #8 #, #9 #, and #2 #. A portion the size of a hemisphere with a radius of #3 # is removed form the ellipsoid. What is the volume of the remaining ellipsoid?

Two rhombuses have sides with lengths of #2 #. If one rhombus has a corner with an angle of #(3pi)/8 # and the other has a corner with an angle of #(7pi)/12 #, what is the difference between the areas of the rhombuses?

A line passes through #(5 ,8 )# and #(2 ,2 )#. A second line passes through #(1 ,3 )#. What is one other point that the second line may pass through if it is parallel to the first line?