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# A Triangle and a Parallelogram Have the Same Base and the Same Area. If the Sides of the Triangle Are 13 Cm, - CBSE Class 9 - Mathematics

ConceptArea of a Triangle by HeronβS Formula

#### 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.

#### 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

π΄πππ ππ Δπ·πΆπΈ = 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 Δππ π·πΆπΈ= ππππ ππ π΄π΅πΆπ·
= Area of parallelogram ABCD = =84cm^2
⇒ 24×β=84 [∴ Area of parallelogram = base × height]
⇒ h = 6 cm

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#### APPEARS IN

Solution A Triangle and a Parallelogram Have the Same Base and the Same Area. If the Sides of the Triangle Are 13 Cm, Concept: Area of a Triangle by HeronβS Formula.
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