# Sadie Adams

Geometry teacher | Verified Expert

Greetings! I'm a dedicated geometry expert, honing my skills at Loyola University Maryland. Passionate about shaping mathematical minds, I thrive on unraveling the complexities of geometry. With a commitment to fostering understanding, I'm here to guide students through the intricacies of shapes, angles, and the beauty of mathematical relationships. Let's embark on a journey of geometric exploration 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 #9/8 #, #3/5 #, and #12 #, respectively. What is the rectangle's area?

A triangle has corners at #(2 , 9 )#, #(3 ,7 )#, and #(1 ,1 )#. What is the radius of the triangle's inscribed circle?

Circle A has a radius of #4 # and a center of #(6 ,1 )#. Circle B has a radius of #2 # and a center of #(5 ,3 )#. If circle B is translated by #<-2 ,2 >#, does it overlap circle A? If not, what is the minimum distance between points on both circles?

Two corners of an isosceles triangle are at #(8 ,3 )# and #(5 ,4 )#. If the triangle's area is #4 #, what are the lengths of the triangle's sides?

If a hexagon has a radius of 6, what is its area?

A triangle has corners A, B, and C located at #(1 ,1 )#, #(6 ,8 )#, and #(7 ,4 )#, respectively. What are the endpoints and length of the altitude going through corner C?

A triangle has corners at #(6 ,5 )#, #(1 ,-6 )#, and #(-2 ,9 )#. If the triangle is dilated by a factor of #5 # about point #(5 ,-5 ), how far will its centroid move?

Given an ellipse with major and minor axis of #a# and #b# find the area of the ellipse? Show your work. the perimeter of the ellipse is rather difficult to derive in closed form, discuss how you would approach it?

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 #42 # and the height of the cylinder is #10 #. If the volume of the solid is #200 pi#, what is the area of the base of the cylinder?

In the figure let #B(20, 0)# and #C(0, 30) #lie in x and y axis respectivelly. The angle, #/_ACB= 90°#. A rectangle DEFG is inscribed in triangle ABC. Given that the area of triangle CGF is 351, calculate the area of the rectangle DEFG?

A triangle has corners at points A, B, and C. Side AB has a length of #48 #. The distance between the intersection of point A's angle bisector with side BC and point B is #16 #. If side AC has a length of #32 #, what is the length of side BC?

A pyramid has a parallelogram shaped base and a peak directly above its center. Its base's sides have lengths of #9 # and #3 # and the pyramid's height is #9 #. If one of the base's corners has an angle of #(5pi)/12#, what is the pyramid's surface area?

A rhombic prism has the diagonal of the rhombus measuring 16 and 12 cm. If the the altitude of the prism is equal in size to the side of the rhombus. What is the surface area and the volume of the Rhombic Prism?

Cups A and B are cone shaped and have heights of #32 cm# and #27 cm# and openings with radii of #12 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?

A circle has a center that falls on the line #y = 3/8x +5 # and passes through # ( 7 ,3 )# and #(2 ,1 )#. What is the equation of the circle?

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

A triangle has corners at #(8 ,3 )#, #(4 ,-6 )#, and #(-2 ,5 )#. If the triangle is dilated by a factor of #5 # about point #(4 ,-3 ), how far will its centroid move?

Circle A has a radius of #4 # and a center at #(8 ,2 )#. Circle B has a radius of #3 # and a center at #(4 ,5 )#. If circle B is translated by #<-3 ,4 >#, does it overlap circle A? If not, what is the minimum distance between points on both circles?

An ellipsoid has radii with lengths of #6 #, #4 #, and #8 #. A portion the size of a hemisphere with a radius of #2 # is removed form the ellipsoid. What is the volume of the remaining ellipsoid?

The area enclosed between the curves y = x^3 and y = √x is in square units ?