Area of a Triangle

One acute angle of a right-angled triangle is double the other. If the length of its hypotenuse is $10 \mathrm{cm}$, then its area is:

Two circles with centres $A$ and $B$ and radius $2 \mathrm{units}$ touch each other externally at $C$. A third circle with centre $C$ and radius $2 \mathrm{units}$ meets other two at $D\hspace{0.17em}\&\hspace{0.17em}E$. Then the area of the quadrilateral $ABDE$ is

$ABCD$ is a parallelogram, $AB=14cm$, $BC=18cm$ and $AC=16cm$. Find the length of the other diagonal.

The perimeter of a triangular field is $450 \mathrm{m}$ and its sides are in the ratio $13 : 12 : 5$. Find the area of the triangle.

Find the area of a haxagon whose side is$4 \mathrm{m}$.

A triangle and a parallelogram are constructed on the same base such that their areas are equal. If the altitude of the parallelogram is $100 \mathrm{m}$, then the altitude of the triangle is?

In $∆\mathrm{ABC}$, $\angle A<\angle B$, the altitude to the base divides vertex angle $C$ into two parts $C_1$ and $C_2$ adjacent to $BC$, then which one of the relation can be obtained?

The sides of a right angled triangle forming right angle are in the ratio $5:2$. If the area of the triangle is$270 {\mathrm{cm}}^2.$ then the length of the hypotenuse is _____.

A chord of a circle of radius $6 \mathrm{cm}$ makes an angles of ${60}^{°}$ at the centre. Area of the minor segment made by the chord is _________.

The perimeter of a triangle $ABC$ is $6$ times the $AM$ of sine of angles of the triangle. Further $BC=\sqrt{3}$ and $CA=1$.

Consider the following statements :

$1.$ $ABC$ is right angled triangle

$2.$ The angles of the triangle are in $AP$

Which of the statements given above is/are correct?

The perimeter of a triangle $ABC$ is $6$ times the $AM$ of sine of angles of the triangle. Further $BC=\sqrt{3}$ and $CA=1$.

What is the perimeter of the triangle?

The area of an equilateral triangle with side $3\sqrt{2} \mathrm{cm}$ is:

X, Y and Z are three equilateral triangles. The sum of the areas of X and Y is equal to the area of Z. If the side lengths of X and Y are $6 \mathrm{cm}$ and $8 \mathrm{cm}$ respectively, then what is the side length of Z?

In an equilateral triangle of side $2\sqrt{3} \mathrm{cm}$, a circle is inscribed touching the sides. What is the area of the remaining portion of the triangle?

Find area of this sector.

Find area of the given triangle:

Find area of the given triangle:

In triangle $\mathrm{PQR},\mathrm{PS}$ is the altitude to $\mathrm{QR}$. Which of the following must be true?

Find the area of a regular Hexagon which has a side of length $12$ units?

Find the area of a regular hexagon that has a side length of $10 \mathrm{units}$.