Question

DPS school provided free education to girl students from weaker sections.
The local body of a town want to open DPS school in the town for which a
rectangular plot ABCD as shown in the figure is very suitable. But this plot
belongs to Sohan Lal. Sohan Lal agrees to exchange it with triangular plot
PQR as shown in the same figure.

1. write the coordinate of point C

2. write the coordinate of point A

3.find the difference between the area of the rectangle and triangle

4. find the area (in sq. units) of rectangle ABCD

5. find the area (in sq. units) of triangle PQR ​

Answer 1

Answer:

1. The coordinates of point C is (3,9),2. the coordinates of point A (3 6), 3.The difference between the area of rectangle and triangle = 11sq.units, 4. the area of rectangle ABCD = 15 sq.units, 5. The area of triangle PQR = 4 sq. units.

Step-by-step explanation: The coordinates of the given points can be found by finding the x- coordinate and the y- coordinate (distance of the point from x- axis and from y-axis) of the point from the graph.

1.The coordinates of point C is (3,9)

2. The coordinates of point A is (3,6).

3. The difference between the area of the rectangle and triangle

=area of rectangle- area of triangle  = 15 - 4 =11 square units.

4. area of rectangle ABCD = l × b .

Here, l is the distance between A and B and it is 5units and b, breadth is the distance between B and C or A and D ,that is 3 units.

Area of the rectangle ABCD = 5×3 =15 square units.

5. The area of the triangle PQR =1/2× b × h .

Here, base b = 4 units and height or altitude h =4 units.

Area of the triangle PQR = 1/2×4×4 = 16/2 = 8 square units.

Answer 2

Answer: 1.coordinate of point $C$ will be (8,9).

2. coordinate of point $A$ will be (3,6).

3.The difference between area of rectangle and area of triangle is $7$ $square$ $unit.$

4.Area of rectangle $ABCD$ $= 15$ $square$ $unit$.

5.    Area of Δ$PQR$ $= 8$ $square$ $unit$.

Step-by-step explanation:

Given: $DPS$ school provided free education to girl students from weaker sections.The local body of a town want to open $DPS$ school in the town for which a rectangular plot $ABCD$ as shown in the figure is very suitable. But this plot belongs to $Sohan$ $Lal$.$Sohan$ $Lal$ agrees to exchange it with triangular plot.

To find: We have to find:1. Write the coordinate of point $C$

2. Write the coordinate of point $A$

3.Find the difference between the area of the rectangle and triangle

4. Find the area (in sq. units) of rectangle $ABCD$

5. Find the area (in sq. units) of triangle$PQR$

Explanation:

Step 1: As the distance of point $C$ on x-axis is 8 and on y-axis is 9.

∴          coordinate of point $C$ will be (8,9).

Step 2:As the distance of point $A$ on x-axis is 3 and on y-axis is 6.

∴          coordinate of point $A$ will be (3,6).

Step 3: The difference between area of rectangle and area of triangle is given by,

                                                  $= 15$ $square$ $unit$ $-$ $8$ $square$ $unit$

                                                  $= 7$ $square$ $unit$

∴The difference between area of rectangle and area of triangle is $7$ $square$ $unit.$

Step 4: Length of rectangle $ABCD$ $= 5 unit$

             Breadth of rectangle $ABCD$ $= 3 unit$

∴ Area of rectangle $ABCD$ $=$ $length$ × $breadth$

                                             $= 5unit$ × $3unit$

                                             $= 15$ $square$ $unit$

∴ Area of rectangle $ABCD$ $= 15$ $square$ $unit$.

Step 5: To find the area of Δ$PQR$ we have to look at the triangle,

             The base of the Δ$PQR$ $= 4unit$

             The height of the Δ$PQR$ $= 4 unit$

∴                            Area of Δ$PQR$ $= \frac{1}{2}$ × $base$ × $height$

                                                       $= \frac{1}{2}$ × $4$ × $4$

                                                       $=\frac{16}{2}$

                                                        $= 8$ $square$ $unit$

∴                            Area of Δ$PQR$ $= 8$ $square$ $unit$.

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