Area of a Quadrilateral

Q.

In parallelogram ABCD, AB = 10 cm. The altitudes corresponding to the sides AB and AD are respectively 7 cm and 8 cm. Find AD. [2 MARKS]

Q.

The area of the region bounded by $\mathrm{y}=2\mathrm{x}-{\mathrm{x}}^2$ and the $\mathrm{x}$-axis.

1. $\frac{8}{3}\mathrm{sq}\mathrm{units}$

2. $\frac{4}{3}\mathrm{sq}\mathrm{units}$

3. $\frac{7}{3}\mathrm{sq}\mathrm{units}$

4. $\frac{2}{3}\mathrm{sq}\mathrm{units}$

Q.

Points $A\left(3,1\right),B\left(12,-2\right)\mathrm{and}C\left(0,2\right)$ cannot be the vertices of a triangle. State whether the following statement is true or false. Justify your answer.

1. True
2. False

Q.

The area (in sq. units) of the largest rectangle $ABCD$ whose vertices $A$ and $B$ lie on the x-axis and vertices $C$ and $D$ lie on the parabola, $y=x^2-1$ below the x-axis, is

1. $\frac{2}{3\sqrt{3}}$

2. $\frac{4}{3}$

3. $\frac{1}{3\sqrt{3}}$

4. $\frac{4}{3\sqrt{3}}$

Q.

If $A(0,0),B(12,0),C(12,2),D(6,7)$ and $E(0,5)$ are the vertices of the pentagon $ABCDE$, then its area (in sq units) is

1. $58$

2. $60$

3. $61$

4. $62$

5. $63$

Q.

A person walked diagonally across a square plot of side 1 m. Approximately, what was the percent saved by not walking along the edges?

1. 35

2. 30

3. 25

4. 20

Q.

A triangle $ABC$ lying in the first quadrant has two vertices as $A\left(1,2\right)$ and $B\left(3,1\right)$ If $BAC=90°$ and $ar\left(∆ABC\right)=5\sqrt{5}$ units, then the abscissa of the vertex $C$ is:

1. $1+\sqrt{5}$

2. $1+2\sqrt{5}$

3. $2\sqrt{5}-1$

4. $2+\sqrt{5}$

Q.

Find the area of the quadrilateral ABCD whose vertices are respectively A (1, 1), B (7, –3) C (12, 2) and D (7, 21).

Q.

Find the area of parallelogram whose base is $10\mathrm{cm}$ and height is $4\mathrm{cm}$. Find the area of parallelogram.

Q.

Calculate the area of a triangle with vertices $\left(1,1\right)$, $\left(3,1\right)$ And $\left(5,7\right)$ .

Q.

Determine whether the following points are collinear or not: A (3, 1), B (6, 4) and C (8, 6) [2 MARKS]

Q. In a circular table cover of radius 32 cm, adesign is formed leaving an equilateral triangle ABC in the middle . Find the area of the design

Q. Question 3
Find area of a triangle formed by joining mid-points of sides of another triangle whose vertices are (0, -1), (2, 1) and (0, 3). Find ratio of this area to the area of the given triangle.

Q. If $A(-5,7),B(-4,-5),C(-1,-6)$ and $D(4,5)$ are the vertices of a quadrilateral, find the area of the quadrilateral $ABCD$.

Q. In triangle ABC, points P and Q trisect side AB. Points T and U trisect side AC and points R and S trisect side BC. Then the perimeter of hexagon PQRSTU is how many times of the perimeter of triangle ABC?

Q. A rectangle ABCD, A = (0, 0), B = (4, 0), C = (4, 2), D = (0, 2) undergoes the following transformations successively.
(i) $f_1(x,y)\to (y,x)$
(ii) $f_2(x,y)\to (x+3y,y)$
(iii) $f_3(x,y)\to (\frac{x-y}{2},\frac{x+y}{2})$
The final figure will be

1. a rhombus
2. a square
3. a rectangle
4. a parallelogram

Q. Find the fourth vertex $D$ of parallelogram $ABCD$ whose three vertices are $A(-2,3),B(6,7)$ and $C(8,3)$.

Q.

If D, E and F are the mid-points of sides BC, CA and AB respectively of a $\Delta ABC$, then using coordinate geometry prove that Area of $\Delta DEF=\frac{1}{4}\left(Areaof\Delta ABC\right)$

Q.

The area of a quadrilateral whose vertices taken in order are (–4, –2), (–3, –5), (3, –2) and (2, 3) is _______.

1. 26 sq. units

2. 30 sq. units

3. 28 sq. units

4. 27 sq. units

Q. Show that four points $(0,-1),(6,7),(-2,3)and(8,3)$ are the vertices of a rectangle. Also, find its area.

Q. Find the area of the quadrilateral whose vertices are
(i).A(2, 1), B(2, 3), C(-2, 2), D(-1, 0)
(ii) A(-3, 1), B(-2, -2), C(4, 1), D(2, 3)

Q. Find the area of the quadrilateral $ABCD$ whose vertices are respectively $A(1,1),$ $B(7,-3)$, $C(12,2)$ and $D(7,21)$?

Q. What is the area of the rhombus formed by (3, 0), (4, 5), (-1, 4) and (-2, -1) as vertices?

1. 16 sq. units
2. 32 sq. units
3. 42 sq. units
4. 24 sq. units

Q. Plot the points A (4, 5), B (-1, 5), C (-1, -2) and D (4, -2) on a graph paper. Join AB, BC, CD and DA. Give a special name to the quadrilateral ABCD obtained. Also, find its area.

Q. Four vertices of a parallelogram taken in order are $(-3,-1),(a,b),(3,3)$ and $(4,3).$ What will be the ratio of a and b ?

1. $4:1$
2. $1:2$
3. $1:3$
4. $3:1$

Q. Find the area of the quadrilateral whose vertices are $(-4,5),(0,7),(5,-5)$ and $(-4,-2).$

Q. Question 8
The area of the square that can be inscribed in a circle of radius 8 cm is
(A) $256c{m}^2$
(B) $128c{m}^2$
(C) $64\sqrt{2}c{m}^2$
(D) $64c{m}^2$

Q.

The area of a quadrilateral whose vertices taken in order are (–4, –2), (–3, –5), (3, –2) and (2, 3) is _______.

1. 26 sq. units

2. 30 sq. units

3. 28 sq. units

4. 27 sq. units

Q. Find the length of the perpendicular drawn from
the point $(-3,-4)$ upon the straight line $12(x+6)=5(y-2)$.

Q. The point $\left(-4,5\right)$ is the vertex of a square and one of its diagonals is $7x-y+8=0$. The equation of the other diagonal is.

1. $7x-y=23$
2. $x+7y=31$
3. $x-7y=31$
4. None of these