isosceles triangle

Geometry-related Problems

Example
An isosceles triangle has an altitude equal to 12 inches and a perimeter equal to 36 inches. Find the length of the base and the length of the equal sides.
 

03 Point P Inside an Isosceles Right Triangle

Problem
Point P is inside the isosceles right triangle ABC. AP is 15 cm, BP is 9 cm and CP is 12 cm as shown. Determine the area of the triangle ABC.
 

034-point-p-inside-isosceles-right-triangle.gif

 

Solved Problem 07 | Cube

Problem 07
Find the area of the triangle whose vertex is at the midpoint of an upper edge of a cube of edge a and whose base coincides with the diagonally opposite edge of the cube.
 

09 Areas outside the overlapping circles indicated as shaded regions

Problem
From the figure shown, AB = diameter of circle O1 = 30 cm, BC = diameter of circle O2 = 40 cm, and AC = diameter of circle O3 = 50 cm. Find the shaded areas A1, A2, A3, and A4 and check that A1 + A2 + A3 = A4 as stated in the previous problem.
 

Circles with centers at midpoints of sides of a right triangle

 

07 Area inside the larger circle but outside the smaller circle

Problem
From the figure shown below, DE is the diameter of circle A and BC is the radius of circle B. If DE = 60 cm and AC = 10 cm, find the area of the shaded region.
 

025-overlapping-circles.gif

 

28 - Solved problem in maxima and minima

Problem 28
The perimeter of an isosceles triangle is P inches. Find the maximum area.
 

 
 
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