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
Find the area of the shaded region in the given figure.
Sides of a triangle are cm 45 cm, 39 cm and 42 cm, find its area.
Find the area of triangle AGF
Using Heron’s formula, find the area of a triangle whose sides are 10 cm, 24 cm, 26 cm
Find the area of an equilateral triangle whose perimeter is 180 cm
Find the area of the unshaded region
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.
The sides of a quadrilateral ABCD are 6 cm, 8 cm, 12 cm and 14 cm (taken in order) respectively, and the angle between the first two sides is a right angle. Find its area.
A field is in the shape of a trapezium having parallel sides 90 m and 30 m. These sides meet the third side at right angles. The length of the fourth side is 100 m. If it costs Rs 4 to plough 1 m2 of the field, find the total cost of ploughing the field.
In the following figure, โABC has sides AB = 7.5 cm, AC = 6.5 cm and BC = 7 cm. On base BC a parallelogram DBCE of same area as that of โABC is constructed. Find the height DF of the parallelogram.
