Question

If the sides of A triangle and a parallelogram have the same base and the the triangle are 26 cm, 28 cm and 30 cm, and the parallelogram stands on the base 28 cm, find the height of the parallelogram.

Answer 1

If the sides of the triangle are 26 cm, 28 cm, and 30 cm, and the parallelogram stands on the base 28 cm, we have found that the height of the parallelogram is 12 cm

= Area of the triangle

formula, we can calculate the height of the parallelogram 

Heron's formula for the area of a triangle is: Area = √s(s - a)(s - b)(s - c)

Where a, b, and c are the sides of the triangle, and s = Semi-perimeter = Half the

Perimeter of the triangle

Let ABCD is a parallelogram and ABE is a triangle having a common base with parallelogram ABCD.

Answer 2

⇝Given :-

Sides of a triangle have same base.

Sides of triangle = 26cm , 28cm , 30cm

Base of parallelogram = 28cm

▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃

⇝To Find :-

Height of parallelogram = ?

▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃

⇝Solution :-

❒ We know that :

${\large{\red{\bigstar \: \: \: \: \: \: {\orange{\underbrace{\underline{\green{\bf{Semi - Perimeter = \frac{a + b + c}{2} }}}}}}}}}$

${\large{\red{\bigstar \: \: \: \: \: \: {\orange{\underbrace{\underline{\green{\bf{Area = \sqrt{s(s - a)(s - b)(s - c)} }}}}}}}}}$

❒ Area of triangle :

✏ Semi - Perimeter :

${\large{:{\longmapsto{\bf{Semi - Perimeter = \frac{a + b + c}{2} }}}} }$

${\large{:{\longmapsto{\bf{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \frac{26 + 28 + 30}{2} }}}} }$

${\large{:{\longmapsto{\bf{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: {\cancel \frac{84}{2} }}}} }}$

${\large{\orange{\dashrightarrow{\blue{\underline{\bf{42 cm}}}}}}}$

✏ Area :

${\large{:{\longmapsto{\bf{Area = \sqrt{s(s - a)(s - b)(s - c)} }}}} }$

${\large{:{\longmapsto{\bf{Area = \sqrt{42(42 - 26)(42 - 28)(42 - 30)} }}}} }$

${\large{:{\longmapsto{\bf{Area = \sqrt{42 \times 16 \times 14 \times 12} }}}} }$

${\large{\orange{\dashrightarrow{\blue{\underline{\bf{336 \: {cm}^{2} }}}}}}}$

❒ Height of parallelogram :

✏ Here :

Base = 28 cm

Area = area of triangle = 336 cm²(given)

Height = ?

✏ Height :

${\large{:{\longmapsto{\bf{Area \: of \: parallelogram = Base \times Height}}}}}$

${\large{:{\longmapsto{\bf{336 = 28 \times height}}}}}$

${\large{:{\longmapsto{\bf{Height = {\cancel\frac{336}{28} }}}}}}$

${\large{\red{:{\twoheadrightarrow{\purple{\underline{\overline{\boxed{\bf{Height = 12 cm}}}}}}}}}}$

❒ Hence :

${\huge{\purple{\underline{\red{\underline{\pink{\pmb{\mathfrak{Height = 12cm}}}}}}}}}$

▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃