# Allison Allen

Geometry teacher | Verified Expert

I hold a degree in Geometry from St. Bonaventure University, where I honed my passion for the intricate world of shapes and spatial relationships. With years of experience in tutoring, I thrive on simplifying complex geometric concepts for students. My goal is to empower learners with a deeper understanding of geometry's practical applications and its beauty in the world around us. Let's explore angles, lines, and polygons together, unlocking the wonders of this fascinating subject.

## Questions

A parallelogram has sides with lengths of #12 # and #4 #. If the parallelogram's area is #36 #, what is the length of its longest diagonal?

Two circles have the following equations #(x -1 )^2+(y -7 )^2= 25 # and #(x +3 )^2+(y +3 )^2= 9 #. Does one circle contain the other? If not, what is the greatest possible distance between a point on one circle and another point on the other?

How do you use Heron's formula to find the area of a triangle with sides of lengths #23 #, #21 #, and #22 #?

Point A is at #(-2 ,5 )# and point B is at #(-3 ,3 )#. Point A is rotated #pi # 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?

How do you find diameter of a circle with area?

Is the slope of the #y# axis infinity?

How do you use Heron's formula to find the area of a triangle with sides of lengths #14 #, #9 #, and #15 #?

Triangle A has an area of #5 # and two sides of lengths #6 # and #7 #. Triangle B is similar to triangle A and has a side of length #15 #. What are the maximum and minimum possible areas of triangle B?

The base of a triangular pyramid is a triangle with corners at #(6 ,7 )#, #(3 ,1 )#, and #(5 ,9 )#. If the pyramid has a height of #8 #, what is the pyramid's volume?

In an isosceles triangle LMN, LM=39cm, NL=39cm and MN = 27cm, how do you calculate the height of the triangle LMN?

A line segment has endpoints at #(8 ,1 )# and #(7 ,5 )#. If the line segment is rotated about the origin by # pi #, translated horizontally by # - 2 #, and reflected about the x-axis, what will the line segment's new endpoints be?

Given two similar triangles with a scale factor of a : b, show the ratio of their perimeters is also a : b?

Describe a sequence of transformations that transform the graph of f(x) into the graph of g(x)? #f(x)=x^2# and #g(x)=(x-4)^2+4#

A line segment with endpoints at #(5, 1)# and #(7, 2)# is rotated clockwise by #pi/2#. What are the new endpoints of the line segment?

A baseball diamond is a square that is 90' on each side. If a player throws the ball from 2nd base to home, how far will the ball travel?

What is the area of an equilateral triangle with a side of 6?

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

What is the approximate distance between points (-7,2) and (11, -5)?

In the figure given below, the side of the square ABCD is 2 cm. E is the midpoint of AB and F is the midpoint of AD. G is a certain point on CF and 3CG＝2GF. What is the area of the shaded triangle BEG, in cm2?

Two corners of a triangle have angles of #(5 pi ) / 12 # and # ( pi ) / 8 #. If one side of the triangle has a length of #4 #, what is the longest possible perimeter of the triangle?