Plane Geometry Problems

Introduction to Plane Geometry Problems
Plane geometry deals with shapes drawn in plane like line, circle, square, rectangle, triangle and parallelogram, polygons. A plane is a flat surface. We can easily draw shapes like square, rectangle, parallelogram and triangle etc. The plane geometry problems can be of any type like perimeter, area, angles measure, missing side length etc.

Problems on Area and Perimeter
Perimeter: In simple language perimeter is the distance covered around outside of a plane shape. Perimeter is calculated by simply adding all the sides around outside of the shape. Perimeter is one dimensional quantity.
example:  Calculate the perimeter of triangle of side length 5cm, 7 cm. 9 cm.
In this case Perimeter = 5+7+9 = 21cm.
Word Problems on Plane Geometry

Problem 1: An equilateral triangle has a perimeter of 51cm. How long is each side of the triangle?
Solution:  In equilateral triangle all the sides are equal.
let a be the side
Perimeter  = sum of all the sides of the triangle
      51 =   a+a+a
=   51 =  3a
=   3a = 51
= 3/3a  = 51/3
       a  = 21 cm.
so each side of the triangle is 21cm.

Problem 2: A room is 20ft. long and 15 ft. wide. How many square tiles of side 5ft. required to cover the floor?
Solution:  Room is a rectangle. Area of rectangle = length x width = 20 x15  sq. ft.
               shape of tile is square. Area of square = side x side     =    5 x 5  sq. ft.

Total area of the floor 20 x 15=300
Area of 1 tile 5x5=25


Mixed Problem on Plane Geometry
1. The radius of a circle is 13 centimeters. What is the circle's circumference?
2. Area of a parallelogram is 66sqm. Find the height if the base is 13m.
3. In an isosceles triangle , angle opposite to equal sides are 70 degree each. Find the measure of the third angle?
4. If the area of a square is 81sq.cm. Find the perimeter?
5. There are two circles of radii 5cm. and 3cm and a rectangle of 4cm inside a square of  side 15cm.  Find the area of remaining portion?