Question

Tanya joined four triangles of cardboard to create a mask of Joker as shown in the given figure(i) . Find the total area of the mask. (Given
2=1.41, 3=1.73) (ii) A design is made on a rectangular tile of dimensions 50 cm × 70 cm as
shown in figure(ii) The design shows 8 triangles, each,of sides 26 cm,
17 cm and 25 cm.Find the total area of the design and the remaining area of the tile.

Answer 1

Given :  Tanya joined four triangles of cardboard to create a mask of Joker as shown in the given figure

To find : total area of the mask

Solution:

i) Ref  attached figure

Area of triangle with side 2  = (√3 / 4)2²   = √3  = 1.73  cm²

Area of two triangles with side 2 cm = 2 * 1.73 =  3.46  cm²

area of triangle with side 6 , 11 & 15 cm

s = (6 + 11 + 15)/2 = 16 cm

Area of triangle use heron formula = √s(s-a)(s-b)(s - c)

= √16(16-6)(16-11)(16 - 15)

= √16 * 10 * 5 * 1

= 20√2

= 20 * 1.41

= 28.2 cm²

area of triangle with side 6 , 15 & 15 cm

s = 18

Area = √18*12*3*3  = 18√3√2= 43.9 cm²

Total area of mask = 3.46 + 28.2 + 43.9  =75.56 cm²

the total area of the mask  = 75.56 cm²

ii)

Area of rectangle = 50 * 70 = 3500 cm²

Area of one triangle with side 17 cm , 25 cm , 26 cm

s = ( 17 + 25 + 26)/2 = 34

Area of one triangle  = √34(34-16)(34-25)(34 - 26)

= √34*17 * 9 * 8

= 17 * 3 * 4

= 204 cm²

area of 8 triangles = 8 * 204  = 1632  cm²

total area of the design = 1632  cm²

Remaining area of tile = 3500 - 1632  = 1868 cm²

Remaining area of tile = = 1868 cm²

Learn more:

a mosaic is desined in the shape of an equilateral triangle 12 ft on ...

https://brainly.in/question/16625279

A wall of the kitchen is 8 metre long and 6 metre wide which is to be ...

https://brainly.in/question/7629960