Area of Triangle

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 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 $k$.

Shown below is a triangular piece of land (No Mans Land) bounded by three roads. Length of the road segment that determines its sides are $5 \mathrm{m}, 5 \mathrm{m}$ and $8 \mathrm{m}$. The corporation widens its roads and the “No Man’s Land" takes the shape of an equilateral triangle of sides $5 \mathrm{m}$.

How much area of the “No man’s land" did the corporation use to widen its road?

Shown below is the design of a floor after tiles of identical shape and size is laid on it. Sides of each tile are $13 \mathrm{inches}, 14 \mathrm{inches} \mathrm{and} 15 \mathrm{inches}$.

What is the minimum number of tiles required to cover the floor area of  $100 \mathrm{sq} \mathrm{inches}$ without any gaps?

Shown below is the well-known region called the ‘Bermuda triangle’. Its sides are approximately, $1400 \mathrm{km}, 1500 \mathrm{km} \mathrm{and} 2100 \mathrm{km}$.

Which of the following represents its area?

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

The perimeter of an isosceles triangle is $32 \mathrm{cm}$. The ratio of one of the equal sides to its base is $3: 2$. If the area of the triangle is $\mathrm{k}\sqrt{2} {\mathrm{cm}}^2$ then find the value of $\mathrm{k}.$

Consider a triangle whose perimeter is $180 \mathrm{cm}$ and two of its sides are of lengths $80 \mathrm{cm}$ and $18 \mathrm{cm}$.If the altitude of the triangle corresponding to the shortest side is $k \mathrm{cm}$.

Then find the value of $k$.

The area of the equilateral triangle if the height of the triangle is $8 \mathrm{cm}$ is$\frac{a}{\sqrt{b}} {\mathrm{cm}}^2$. Find the value of $a+b$.

If the area of an equilateral triangle of side $8 \mathrm{cm}$ is $\mathrm{k}\sqrt{3 }{\mathrm{cm}}^2$ then find the value of $\mathrm{k}$.

If the perimeter of an equilateral triangle is $90 \mathrm{m}$ and if the area of equilateral triangle is $\mathrm{k}\sqrt{3}{\mathrm{m}}^2$ then find the value of $\mathrm{k}$.

If the area of the triangle whose sides are $1.6 \mathrm{cm}$, $3 \mathrm{cm}$ and $3.4 \mathrm{cm}$ is $k {\mathrm{cm}}^2$.

Then find the value of $k$.

If the area of the given triangle is $k {\mathrm{cm}}^2$.

Then find the value of $k$.

Shown below is the design of a floor after tiles of identical shape and size is laid on it. Sides of each tile are 13 inches, 14 inches and 15 inches.

What is the minimum number of tiles required to cover the floor(area) 100 sq ft without any gaps?

Shown below is a triangular piece of land (No Mans Land) bounded by three roads. Length of the road segment that determine its sides are 5 m, 5 m and 8 m.

The corporation widens its roads and the “No Man’s Land" takes the shape of an equilateral triangle of sides 5 m.

How much area of the “No man’s land" did the corporation use to widen its road?

(Note: Round your answer to the nearest whole number.)

The perimeter of the top surface of the given stool is 84 inches. Two of its sides are 26 and 28 inches. The top surface of the stool is covered with a cloth up to a depth of 3 inches (observe the extended sides of the cloth) as shown below.

Sunil needs to buy a cloth piece to stich a cover for the stool. Its width is 3 ft.

What is the shortest length of the cloth that Sunil needs to buy?

(Note: Assume 1 inch = 2.54 cm and 1ft = 12 inches. Round your answer to nearest whole number. )

Shown below is the well known region called the ‘Bermuda triangle’.

Its sides are approximately, $1400 \mathrm{km}, 1500 \mathrm{km}$ and $2100 \mathrm{km}$

Which of the following represents its area?

Shown below is a triangular shaped table. Its top surface is laminated with a thin sheet of wooden material of sides 42 inches, 20 inches and 34 inches.

Calculate the cost of laminating its top surface, if the material costs &rupee;60 per sq ft.

The cost of lamination is &rupee;_____ .

(Note: 1 feet = 12 inches.)