Area of a Triangle

Find the area (in sq. unit) of the triangle formed by joining midpoints of the sides of the triangle whose vertices are $\left(0, -1\right), \left(2, 1\right)$ and $\left(0, 3\right)$. 

The area of a triangle $ABC$ is $k {\mathrm{cm}}^2$, whose vertices (in $\mathrm{cm}$) are $A\left(4, 4\right), B\left(0, 0\right)$ and $C\left(6, 2\right)$. Now, find the value of $k$? 

Find the numerical value of the area of a rhombus $ABCD$, if its vertices are $A\left(3, 0\right), B\left(4, 5\right), C\left(-1, 4\right), D\left(-2, -1\right)$.

Find the value(s) of x for which distance between the point $P\left(2, -3\right)$ and $Q\left(x, 5\right)$ is $10$.

Find the numerical value (without unit) of the area of a triangle $ABC$, whose vertices are $A\left(1, -1\right), B\left(-4, 6\right)$ and $C\left(-3, -5\right)$.

Find the area of the triangle formed by joining midpoints of the sides of the triangle whose vertices are $\left(0, 1\right), \left(2, 1\right), \left(0, 3\right)$. Find the ratio of this area to the area of the given triangle.

Find the numerical value (without unit) of the area of quadrilateral $ABCD$, formed by the joining of the following points in order $A\left(2, 9\right), B\left(3, 5\right), C\left(5, 5\right), D\left(7, 9\right)$.

Find the numerical value (without unit) of the area of quadrilateral $ABCD$, formed by the following points $A\left(4,3\right), B\left(6,4\right), C\left(5,-6\right), D\left(3,-7\right)$.

The points $A(2,9), B(a,5), C(5,5)$ are the vertices of a triangle $ABC$, right angled at $B$. Find the value of $a$ and hence find the are of $△ABC$.

If $A\left(4,-6\right),B\left(3,-2\right)$ and $C\left(5,2\right)$ are the vertices of a $△ABC$, then verify the fact that a median of $△ABC$ divides it into two triangles of equal areas.

If the vertices of a triangle are $\mathrm{A} (2, 4), \mathrm{B} (5, \mathrm{k}) \mathrm{and} \mathrm{C} (3, 10)$ and its area is $15 \mathrm{square} \mathrm{units}$ then find the value of $k.$

If $A(-5, 7), B(-4, -5), C(-1, -6) \mathrm{and} D(4, 5)$ are the vertices of the quadrilateral $ABCD,$ find the numerical value of the area of the quadrilateral $ABCD$.

If the area of the quadrilateral whose vertices are $(-4,-2), (-3,-5), \left(0,-5\right) \mathrm{and} \left(2,-2\right)$ is $k {\mathrm{cm}}^2$. Find the value of $k$.

The area of a triangle with vertices $A(3, 0), B(7, 0)$ and $C(8, 4)$ is

The perimeter of a triangle with vertices $(0, 4), (0, 0)$ and $(3, 0)$ is

The area of the triangle formed by $(a, b+c), (b, c+a)$ and $(c, a+b)$ is

$A, B, C$ are the points $(-1, 5), (3, 1)$ and $(5, 7)$ and $D, E, F$ are the midpoints of $BC, CA$ and $AB$ respectively. Prove that $∆ABC$ is equal to four times of area of $∆DEF$.

$A, B$ are the two points $(3, 4)$ and $(5, -2)$ . Find the point $P$ such that $PA=PB$ and the area of $∆PAB$ is equal to $10$.

If the length of the altitude of the triangle is$\frac{24}{\sqrt{k}}$ , coordinates of whose vertices are $(5, 1), (2, 4)$ and $(-1, -1)$.

Find the value of $k$.

If the area of the triangle formed by the following points is $k^2 \mathrm{sq}. \mathrm{unit}$ then find $k$.

$(a, c+a), (a, c)$ and $(-a, c-a)$