isosceles triangle

Geometry-related Problems

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

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.



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

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

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.



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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