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.
Answers
Area of mask = 71.45 sq. cm.
Step-by-step explanation:
Area of upper triangle of side 2 cm.
Base = 2/1 = 1 cm.
Height = √2² - 1² = √3 = 1.73 cm
2 * Area of upper triangle = 2* 1/2 * 1 * 1.73 = 2 * 1.73/2 = 1. 73 sq. cm
Area of lower left triangle:
Area= √s(s−a)(s−b)(s−c)
s = a + b + c / 2
s = 6 + 11 + 15 / 2 = 32/2 = 16
Area = √16(16−6)(16−11)(16−15)
= √16(10)(5)(1)
= √800
= 20*√2
= 28.2 sq. cm
Area of lower right triangle by Heron's formula:
s = 6 + 15 + 15 /2 = 18
Area = √18(18−6)(18−15)(18−15)
= √16(12)(3)(3)
= 4*3 * 2 * √3
= 41.52 sq. cm.
Area of mask = 1.73 + 28.2 + 41.52
= 71.45 sq. cm.
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
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