# Sophia Alfred

Geometry teacher | Experienced educator in USA

I'm a Geometry expert, graduating from Shepherd University. My passion lies in unlocking the mysteries of shapes and spaces. With a knack for simplifying complex concepts, I empower students to conquer geometric challenges with confidence. Let's navigate the world of angles and proofs together!

## Questions

A line segment goes from #(3 ,1 )# to #(2 ,4 )#. The line segment is dilated about #(2 ,2 )# by a factor of #3#. Then the line segment is reflected across the lines #x = 4# and #y=-1#, in that order. How far are the new endpoints form the origin?

How do you use Heron's formula to find the area of a triangle with sides of lengths #5 #, #5 #, and #5 #?

A triangle has corners at points A, B, and C. Side AB has a length of #15 #. 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 #24 #, what is the length of side BC?

Point A is at #(5 ,-2 )# and point B is at #(-2 ,5 )#. Point A is rotated #pi/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 vertices A, B, and C. Vertex A has an angle of #pi/12 #, vertex B has an angle of #(pi)/2 #, and the triangle's area is #2 #. What is the area of the triangle's incircle?

Two corners of an isosceles triangle are at #(9 ,2 )# and #(1 ,7 )#. If the triangle's area is #64 #, what are the lengths of the triangle's sides?

Two opposite sides of a parallelogram each have a length of #4 #. If one corner of the parallelogram has an angle of #(11 pi)/12 # and the parallelogram's area is #42 #, how long are the other two sides?

Given the right trapezoid calculate angle #theta# and the area of triangle #hat(EAD)#, provided #EA=4, AB=BC=CD=DA=2, AB_|_EC#?

An ellipsoid has radii with lengths of #15 #, #12 #, and #9 #. 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?

A triangle has corners at points A, B, and C. Side AB has a length of #42 #. The distance between the intersection of point A's angle bisector with side BC and point B is #9 #. If side AC has a length of #45 #, what is the length of side BC?

What is the area of a circle which diameter is 8.5m?

What is the perimeter of a rhombus whose diagonals are 16 and 30?

Circle A has a center at #(2 ,3 )# and a radius of #5 #. Circle B has a center at #(3 ,8 )# and a radius of #1 #. Do the circles overlap? If not what is the smallest distance between them?

A parallelogram has sides A, B, C, and D. Sides A and B have a length of #2 # and sides C and D have a length of # 1 #. If the angle between sides A and C is #(7 pi)/18 #, what is the area of the parallelogram?

How do you use Heron's formula to find the area of a triangle with sides of lengths #11 #, #14 #, and #18 #?

What is the perimeter of a triangle with corners at #(7 ,5 )#, #(1 ,2 )#, and #(4 ,8 )#?

A circle has a chord that goes from #( pi)/3 # to #(2 pi) / 3 # radians on the circle. If the area of the circle is #16 pi #, what is the length of the chord?

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?

If length and breadth of a rectangle is doubled, what happens to its perimeter?