Advertisements
Advertisements
प्रश्न
Complete the hexagonal and star shaped rangolies (see the given figures) by filling them with as many equilateral triangles of side 1 cm as you can. Count the number of triangles in each case. Which has more triangles?
Advertisements
उत्तर
It can be observed that hexagonal-shaped rangoli has 6 equilateral triangles in it.
`"Area of "ΔOAB = sqrt3/4"(side)"^2`
`= sqrt3/4(5)^2`
`= sqrt3/4(25)`
`= (25sqrt3)/4cm^2`
`"Area of hexagonal-shaped rangoli "=6xx(25sqrt3)/4=(75sqrt3)/2cm^2`
`"Area of equilateral triangle having its side as 1cm "=sqrt3/4(1)^2=sqrt3/4cm^2`
`"Number of equilateral triangles of 1 cm side that can be filled in this hexagonal-shaped rangoli "=((75sqrt3)/2)/(sqrt3/4)=150`
Star-shaped rangoli has 12 equilateral triangles of side 5 cm in it.
`"Area of star-shaped rangoli "=12xxsqrt3/4xx(5)^2=75sqrt3`
`"Number of equilateral triangles of 1 cm side that can be filled in this star-shaped rangoli "=(75sqrt3)/(sqrt3/4)=300`
Therefore, star-shaped rangoli has more equilateral triangles in it.
संबंधित प्रश्न
Show that in a right angled triangle, the hypotenuse is the longest side.
AB and CD are respectively the smallest and longest sides of a quadrilateral ABCD (see the given figure). Show that ∠A > ∠C and ∠B > ∠D.
In a triangle locate a point in its interior which is equidistant from all the sides of the triangle.
In the following figure, write BC, AC, and CD in ascending order of their lengths.
In the following figure ; AC = CD; ∠BAD = 110o and ∠ACB = 74o.
Prove that: BC > CD.
Prove that the perimeter of a triangle is greater than the sum of its three medians.
ABCD is a quadrilateral in which the diagonals AC and BD intersect at O. Prove that AB + BC + CD + AD < 2(AC + BC).
ABCD is a trapezium. Prove that:
CD + DA + AB > BC.
In the given figure, T is a point on the side PR of an equilateral triangle PQR. Show that PT < QT
In the given figure, T is a point on the side PR of an equilateral triangle PQR. Show that RT < QT
