Area of Triangle Using Heron's Formula

A field is in the quadrilateral shape $abcd$. Its sides are $ab= 13 \mathrm{cm}, bc=14 \mathrm{cm}, cd=20 \mathrm{cm}$ and $ad = 25 \mathrm{cm}$. The length of the diagonal $ac$ is $15 \mathrm{cm}$. Find the area of the quadrilateral.

A triangular filed has sides which are in a ratio of $9:10:11$ and an area of $270\sqrt{2}{\mathrm{cm}}^2$. Find the sides of this triangle.

The sides of a triangular field are $65 \mathrm{m}, 156 \mathrm{m} \text{and} 169 \mathrm{m}$. A parallelogram having base as the longest side of triangle has same area then height of the parallelogram will be $6 k$. What is the value of $k$.  

If the area of a triangle's field where the sides are $60 \mathrm{m}, 100 \mathrm{m}, 140 \mathrm{m}$ using Heron's formula is $\mathrm{k} {\mathrm{m}}^2$. Find the value of $k$.

In $△ABC$, $AB=15, BC=13$ and $AC=14$. Find its area.

What is heron's formula

The area of triangular park having sides $50\mathrm{m}, 80\mathrm{m}, 120\mathrm{m}$ is:

If the cost of laying grass in a triangular field of sides $50 \mathrm{m}, 65 \mathrm{m}$ and $65 \mathrm{m}$ at the rate of $₹7\text{ per }{\mathrm{m}}^2$ is $₹k$, then find the value of $k$.

A kite in the shape of a square with each diagonal $36 \mathrm{cm}$ and having a tail in the shape of an isosceles triangle of base $10 \mathrm{cm}$ and each side $6 \mathrm{cm}$, is made of three different shades as shown in the figure. If the sum of all shades of paper is $k {\mathrm{cm}}^2$.

Then find the value of $k$ correct to decimal places.

 [Take $\sqrt{11}=3.31$ ]

If the area of the shaded region is $k {\mathrm{cm}}^2$.

Then find the value of $k$.

The base of an isosceles triangle is $4 \mathrm{cm}$ and its area is $16 {\mathrm{cm}}^2$. The semi-perimeter of the triangle is $k \mathrm{cm}.$ The value of $k-1.24$ is

A floral design on a floor is made up of 16 triangular tiles, each having sides $10 \mathrm{cm}, 34 \mathrm{cm}$ and $36 \mathrm{cm}$. Find the cost of
polishing the tiles at the rate of $₹2.50 \mathrm{per} {\mathrm{cm}}^2$. [ Take $\sqrt{2}=1.414$]

A park is in the shape of a quadrilateral $ABCD$ having $AB=9 \mathrm{cm}, \mathrm{BC}=12 \mathrm{cm}, \mathrm{CD}=5 \mathrm{cm}, \mathrm{AD}=8\mathrm{cm}$ and $\angle C={90}^{\circ }$.If the area of the park is $k {\mathrm{cm}}^2$.  [Take $\sqrt{35}=5.9$]

Then find the value of $k$ correct to two decimal places.

Find the cost of levelling the ground in the form of a triangle having its sides $90 \mathrm{m}, 70 \mathrm{m}$ and $70 \mathrm{m}$ at $₹5$ per square meter.

The sides of a triangular plot are in the ratio of $3:5:7$ and its perimeter is $300 \mathrm{m}$. If the area is $\mathrm{k}\sqrt{3}{\mathrm{m}}^2$ then write the value of $\mathrm{k}$.

The sides of a triangular field measure$51 \mathrm{m}, 37 \mathrm{m}$ and $20 \mathrm{m}$. The cost of levelling it at $₹5 per {\mathrm{m}}^2$ is$₹k$ . The value of $\frac{k}{15}$ is

The area of a triangle, two sides of which are $8 \mathrm{cm}$ and $11 \mathrm{cm}$and the perimeter is $32 \mathrm{cm}$ is $k\sqrt{30} {\mathrm{cm}}^2$. Find the value of $k$.

Area of the triangle whose sides are $18 c\mathrm{m}, 24 \mathrm{cm}$ and $30 \mathrm{cm}$ is $36k {\mathrm{cm}}^2$. Find $k$.

The sides of a $\Delta ABC$ are in the ratio $2:4:4$ and its perimeter is $40 \mathrm{cm}$. Then, $ar\left(\Delta ABC\right)=k\sqrt{15} {\mathrm{cm}}^2$ . The value of $k$ is

The area of an isosceles triangle having base $=20 \mathrm{cm}$ and each of the equal sides equal to $14 \mathrm{cm}$ is $k {\mathrm{cm}}^2$. Then value of $k-0.98$ is