Area Related Constructions

Construct a square of sides $6 \mathrm{cm}$ and then construct a triangle of area equal to the area of this square.

Construct a quadrilateral $ABCD$ of which $AB=5 \mathrm{cm}, BC=6 \mathrm{cm}, CD=4 \mathrm{cm}, DA=3 \mathrm{cm}$ and $\angle ABC=60°$. Then construct a triangle of area equal to the area of that quadrilateral.

Construct a triangle of sides $5 \mathrm{cm}, 8 \mathrm{cm}$ and$11 \mathrm{cm}$ and then construct a parallelogram the area of which is equal to the area of that triangle and one of whose angles is $60°$.

In $△PQR, \angle PQR=30°, \angle PRQ=75°$ and $QR=8 \mathrm{cm}$. Construct a rectangle, the area of which is equal to the area of the $△PQR$.

Construct an equilateral triangle of sides $6.5 \mathrm{cm}$ and construct a parallelogram, the area of which is equal to the area of which is equal to the area of the triangle and one of that triangle and one of whose angles is $45°$.

Diagonal divides a parallelogram into two triangles of equal area.

_____ divides the quadrilateral parallelogram into two equal area triangles. 

All kinds of quadrilaterals can be divided into two triangles of equal area.

Is it possible to dividing a quadrilateral into two triangles of equal area, if possible what kind of quadrilateral it is?

Which is the correct diagram for the given construction? 

Draw an isosceles triangle whose equal sides are of length $7 \mathrm{cm}$ and angle between them is $30°$. Draw a rectangle whose area is equal to that triangle.

Which is the correct diagram for the given construction?

Length of each equal sides of an isosceles triangle $8 \mathrm{cm}$ and length of base is $5 \mathrm{cm}$. Draw a parallelogram equal in area to that triangle and having one angle of parallelogram is equal to one of equal angle of isosceles triangle and one side is half of equal side.

Which is the correct diagram for the given construction?

Draw an isosceles triangle whose equal sides are of length $8 \mathrm{cm}$ and angle between them is $30°$. Draw a rectangle whose area is equal to that triangle.

Draw an isosceles triangle whose equal sides are of length $7 \mathrm{cm}$ and angle between them is $30°$. Draw a rectangle whose area is equal to that triangle.

In $△PQR, \angle PQR=30°, \angle PRQ=\angle 75°$ and $QR=7 \mathrm{cm}$. Draw a rectangle equal in area to that triangle.

Construct a parallelogram of area equal to the area of the pentagon $\mathrm{ABCDE}$ and one of whose angles is $60°$.

Select the correct order of construction of rectangle if area equal to the area of $△\mathrm{ABC}$ is constructed with $\angle \mathrm{ABC}=30°, \angle \mathrm{ACB}=75° \mathrm{and} \mathrm{BC}=10 \mathrm{cm}$. 

Step 1: Draw a line parallel to $\mathrm{BC}$ through $\mathrm{A}$. The perpendicular bisector cuts parallel line through $\mathrm{A}$ at $\mathrm{E}$.

Step 2: Draw a perpendicular bisector of side $\mathrm{BC}$, which intersects $\mathrm{BC}$ at $\mathrm{D}$. Join $\mathrm{A}$ to $\mathrm{D}$.

Step 3: Mark the point as $\mathrm{F}$. Join $\mathrm{F}$ to $\mathrm{C}$. $\mathrm{DCFE}$ is the required rectangle.

Step 4: From $\mathrm{E}$, cut an arc of length $\mathrm{DC}$ on the parallel line.

Length of each equal sides of an isosceles triangle $7 \mathrm{cm}$ and length of base is $4 \mathrm{cm}$. Draw a parallelogram equal in area to that triangle and having one angle of parallelogram is equal to one of equal angle of isosceles triangle and one side is half of equal side.

Select the correct order of the steps of construction of a parallelogram of one angle $45°$ and area equal to the area of the $△\mathrm{ABC}$ is constructed with $\mathrm{AB}=\mathrm{BC}=6.5 \mathrm{cm}, \angle \mathrm{ABC}=60°$. 

Step 1: The line $\mathrm{GD}$ cuts parallel line through $C$ at $\mathrm{E}$.

Step 2: Join $\mathrm{F}, \mathrm{B}$. $\mathrm{DBFE}$ is the required parallelogram.

Step 3: Draw a line parallel to $\mathrm{AB}$ through $\mathrm{C}$. At $\mathrm{D}$, construct an angle $\angle \mathrm{GDB}=45°$.

Step 4: Draw a perpendicular bisector of side $\mathrm{AB}$, which intersects $\mathrm{AB}$ at $\mathrm{D}$. Join $\mathrm{C} \mathrm{and} \mathrm{D}$.

Step 5: From $\mathrm{E}$, cut an arc of length $\mathrm{DB}$ on the parallel line. Mark the point as $\mathrm{F}$.

Construct a triangle of equal area of a rectangle $\mathrm{ABCD}$, where $\mathrm{AB}=6 \mathrm{cm}$ and $\mathrm{BC}=4 \mathrm{cm}$ is constructed. If the base of the rectangle is $\mathrm{AB}$, then the length of base of the triangle will be

Draw an equilateral triangle with length of side $5.2 \mathrm{cm}$ and draw a parallelogram equal in area to that triangle and having an angle $45°$.