Advertisements
Advertisements
Question
A triangle and a parallelogram have the same base and the same area. If the sides of the triangle are 13 cm, 14 cm and 15 cm and the parallelogram stands on the base 14 cm, find the height of the parallelogram.
Advertisements
Solution
The sides of a triangle DCE are
DC = 15 cm, CE = 13 cm, ED = 14 cm
Let h be the height of parallelogram ABCD
Given,
Perimeter of ΔDCE
2s = DC + CE + ED
`⇒S=1/2(15+13+4)`
`⇒s=1/2(42)`
`⇒s=21cm`
๐ด๐๐๐ ๐๐ Δ๐ท๐ถ๐ธ = `sqrt(s(s-dc)(s-ce)(s-ed))`
`=sqrt(21(21-15)(21-13)(21-14))`
`=sqrt(21xx7xx8xx6)`
`=sqrt(84xx84)`
`84 cm^2`
Given that
Area of Δ๐๐ ๐ท๐ถ๐ธ= ๐๐๐๐ ๐๐ ๐ด๐ต๐ถ๐ท
= Area of parallelogram ABCD = =`84cm^2`
⇒ 24×โ=84 [∴ Area of parallelogram = base × height]
⇒ h = 6 cm
APPEARS IN
RELATED QUESTIONS
A traffic signal board, indicating ‘SCHOOL AHEAD’, is an equilateral triangle with side ‘a’. Find the area of the signal board, using Heron’s formula. If its perimeter is 180 cm, what will be the area of the signal board?
The triangular side walls of a flyover have been used for advertisements. The sides of the walls are 122m, 22m, and 120m (see the given figure). The advertisements yield an earning of โน 5000 per m2 per year. A company hired one of its walls for 3 months. How much rent did it pay?
An isosceles triangle has perimeter 30 cm and each of the equal sides is 12 cm. Find the area of the triangle.
A triangle has sides 35 cm, 54 cm and 61 cm long. Find its area. Also, find the smallest of its altitudes ?
The perimeter of an isosceles triangle is 42 cm and its baše is (32) times each of the equal sides. Find the length of each side of the triangle, area of the triangle and the height of the triangle.
Find the area of the shaded region in the given figure.
Find the areas of the given plot. (All measures are in metres.)
Determine whether the sets of points are collinear?
(a, b + c), (b, c + a) and (c, a + b)
A man walks near a wall, such that the distance between him and the wall is 10 units. Consider the wall to be the Y-axis. The path travelled by the man is
The cost of levelling the ground in the form of a triangle having the sides 51 m, 37 m and 20 m at the rate of Rs 3 per m2 is Rs 918.
