(B) Given sides are $a = 4 \text{ cm}$,$b = 5 \text{ cm}$,and $c = 7 \text{ cm}$.First,calculate the semi-perimeter $s$:$s = \frac{a + b + c}{2} = \fr

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(B) Given sides are $a = 4 \text{ cm}$,$b = 5 \text{ cm}$,and $c = 7 \text{ cm}$.First,calculate the semi-perimeter $s$:$s = \frac{a + b + c}{2} = \frac{4 + 5 + 7}{2} = \frac{16}{2} = 8 \text{ cm}$.Using Heron's formula,the area of the triangle is:$\text{Area} = \sqrt{s(s - a)(s - b)(s - c)}$$= \sqrt{8(8 - 4)(8 - 5)(8 - 7)}$$= \sqrt{8 \times 4 \times 3 \times 1}$$= \sqrt{96}$$= \sqrt{16 \times 6}$$= 4 \sqrt{6} \text{ cm}^2$.

Class 11 Mathematics Straight Line Problems related to triangle and quadrilateral

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$A$ farmer owns a triangular plot in Guntur. He measures the lengths of the sides of his property as $4 \text{ cm}$,$5 \text{ cm}$,and $7 \text{ cm}$. Then the area of land of the farmer in $\text{sq. cm}$ is

AP EAMCET 2022 All AP EAMCET

A
$2 \sqrt{6}$
B
$4 \sqrt{6}$
C
$\sqrt{6}$
D
$8 \sqrt{6}$

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Problems related to triangle and quadrilateral

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$A$ farmer owns a triangular plot in Guntur. He measures the lengths of the sides of his property as $4 \text{ cm}$,$5 \text{ cm}$,and $7 \text{ cm}$. Then the area of land of the farmer in $\text{sq. cm}$ is

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The equations of the sides $AB$,$BC$ and $CA$ of a triangle $ABC$ are $2x + y = 0$,$x + py = 39$ and $x - y = 3$ respectively and $P(2, 3)$ is its circumcentre. Then which of the following is $NOT$ true?

The area of the triangle enclosed by the straight lines $x = 0$,$y = 0$ and $x + 2y + 3 = 0$ in sq. units is:

The points $(1,3)$ and $(5,1)$ are two opposite vertices of a rectangle. The other two vertices lie on the line $y = 2x + c$,where $c$ is a constant. The coordinates of the other two vertices are:

Two sides of a parallelogram are along the lines $x + y = 3$ and $x - y + 3 = 0$. If its diagonals intersect at $(2, 4)$,then one of its vertices is

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