# Evelyn Arboleda

Geometry teacher | Verified Expert

I hold a degree in Geometry from Dakota State University. My passion lies in unraveling the intricacies of shapes and space, guiding students through the wonders of geometric concepts. With a knack for simplifying complex ideas, I foster a supportive learning environment where students thrive. Whether exploring angles, polygons, or proofs, I'm dedicated to illuminating the beauty and logic of Geometry. Let's embark on this geometric journey together!

## Questions

How do you find the equation of a circle in standard form given #x^2+y^2+4x+6y+4=0#?

What is the orthocenter of a triangle with corners at #(1 ,3 )#, #(5 ,7 )#, and (2 ,3 )#?

Two opposite sides of a parallelogram each have a length of #15 #. If one corner of the parallelogram has an angle of #(5 pi)/12 # and the parallelogram's area is #160 #, how long are the other two sides?

A cone has a height of #11 cm# and its base has a radius of #7 cm#. If the cone is horizontally cut into two segments #8 cm# from the base, what would the surface area of the bottom segment be?

Are these two lines parallel, perpendicular, or neither? Explain. #9x+3y=8#, #3x+9y=8#

A line segment has endpoints at #(2 ,3 )# and #(8 ,9 )#. If the line segment is rotated about the origin by #( pi)/2 #, translated vertically by #-8 #, and reflected about the x-axis, what will the line segment's new endpoints be?

What is the area of a circle with a diameter of 27 inches?

If the diameter of a sphere is 10, what is the approximate volume of the sphere?

What is the area of an equilateral triangle whose vertices lie on a circle with radius 2?

The base of a triangular pyramid is a triangle with corners at #(8 ,5 )#, #(7 ,2 )#, and #(4 ,6 )#. If the pyramid has a height of #7 #, what is the pyramid's volume?

Two opposite sides of a parallelogram each have a length of #9 #. If one corner of the parallelogram has an angle of #(3pi)/8 # and the parallelogram's area is #26 #, how long are the other two sides?

How many diagonals does a convex polygon of #n# sides have?

A parallelogram has sides with lengths of #21 # and #12 #. If the parallelogram's area is #42 #, what is the length of its longest diagonal?

What do you call a polygon with 20 sides?

A solid consists of a cone on top of a cylinder with a radius equal to that of the cone. The height of the cone is #66 # and the height of the cylinder is #5 #. If the volume of the solid is #243 pi#, what is the area of the base of the cylinder?

A circle has a chord that goes from #( pi)/4 # to #(13 pi) / 8 # radians on the circle. If the area of the circle is #27 pi #, what is the length of the chord?

Two corners of an isosceles triangle are at #(8 ,5 )# and #(9 ,1 )#. If the triangle's area is #12 #, what are the lengths of the triangle's sides?

Two rhombuses have sides with lengths of #1 #. If one rhombus has a corner with an angle of #(7pi)/12 # and the other has a corner with an angle of #(3pi)/4 #, what is the difference between the areas of the rhombuses?

A line passes through #(3 ,6 )# and #(6 ,5 )#. A second line passes through #(4 ,3 )#. What is one other point that the second line may pass through if it is parallel to the first line?

If 3 times the supplement of an angle is subtracted from 7 times the complement of the angle, the answer is the same as that obtained from trisecting a right angle. What is the supplement of this angle?