Math Guide

High School Geometry Worksheets

we use high school geometry in our routine life in several situations. For example, we measure the length of a cloth for stitching, the area of a wall for white washing and the volume of a container for filling. High school geometry is the branch of mathematics concerned with the properties of lines, curves, and surfaces usually divided into pure, algebraic, and differential geometry in accordance with mathematical techniques utilized. High school geometry problems are worked out in worksheets.Let us learn solved problems high school geometry worksheets.

High school geometry worksheets problems:

Ex 1:    Theperimeter of a rhombus is 20 cm. One of the diagonals is of length 8 cm. Find the length of the another diagonal and the area of the rhombus.

Sol :       Let d1 and d2 be the diagonal's length.

              Then perimeter = 2√d12+d22.

              But the perimeter is 20 cm. 

              2√d12+d22 = 20 cm or  d12+d22 =100.

              Here one of the diagonals is of length 8 cm.

              Take d1=8. Then 64+d22=100 or d22=36.

                                                              d2=6 cm.

              The area of the rhombus is `(1)/(2)` `(d1* d2)` =`(1)/(2)`  x 8 x6

                                                                       = 24 cm2.


Ex 2:  A wall in the form of a rectangle has base 15m and height 10m. If the cost of painting the wall is Rs. 16 per square meter, find the cost for painting the entire wall.

Sol :       Let b="15" and h="10.
Then the area of the rectangle = `b*h ` = 15 x 10

= 150 sq. meters.

Since the cost of painting 1sq. meter is Rs. 16,

The cost for painting the entire wall = 16 x 150 

= Rs. 2400.

Ex 3:     Thedimensions of a rectangular metal sheet are 6m × 3m. The sheet is to becut into square sheets each of side 6 cm. Find the number of square sheets.

Sol :      Area of the metal sheet = 600×300 = 18,0000 cm2.

              Area of a square sheet = 6×6 = 36 cm2.

              Number  of square sheets =180000/36 = 5000.

Ex 4 :     The radius of a right circular cylinder is 6 cm and its height is 25 cm. Find its curved surface area and total surface area.

Sol :      Radius(r)=6cm, Height(h)=25cm.

                Curved surface area =(2r h) =2⋅227⋅6⋅25 cm2  

                                                                    = 942cm2

                Area of the base and the top    =(2 r2)

                                                                       =2⋅(227)⋅6⋅6 cm2

                                                                       =226 cm2

                Total surface area = (2rh) + (2r2) = 942cm2 + 226cm2

                                                                            = 1168 cm2   


Ex 5 :    The base diameter of  right circular cylinder is 7 cm, height is 40 cm, find volume.

Sol :       Since the diameter of the base is 7 cm, its radius r = 7 / 2 cm. Also, h = 40 cm,

                 and π =22 / 7. Therefore, the volume of the cylinder is given by

                            V = πr2h

                               =(227)⋅(72)⋅(72)⋅40 cm

                               = 1540 cm3