Question

Construct a rhombus each side of which is

4 cm

and one of whose angles is

60 °

. Then construct a triangle of area equal to the area of this rhombus and one of the angles is

45 °

.

Accepted Answer

We know that, in a rhombus all sides are of equal length.
We know that, opposite angles are equal in rhombus and adjacent angles are supplementary.

Construction of rhombus:
Draw a line $AB = 4 cm$ .
From the vertex $A$ , construct $60 °$ by using compass and ruler.
With the compass draw an arc of length $AD = 4 cm$ .
From point $B$ , construct an angle $(180 ° - 60 ° = 120 °)$ .
With the compass mark an arc of length $BC = 4 cm$ .
Draw a line parallel to $AB$ and join the points $CD$ .
$ABCD$ is the rhombus.

Construction of triangle:
Draw a diagonal $BD$ .
Let us draw a line $CG$ through $C$ , parallel to $BD$ .
Produce $AB$ , which intersects $CG$ at $E$ .
Join $D and E$ .
Thus, $ADE$ gives the required triangle.

Construct a rhombus each side of which is $4 cm$ and one of whose angles is $60 °$ . Then construct a triangle of area equal to the area of this rhombus and one of the angles is $45 °$ .

Important Questions on Construction-Drawing of Triangles Equal to the Area of a Given Quadrilateral

Learn and Prepare for any exam you want !

Construct a rhombus each side of which is 4 cm and one of whose angles is 60°. Then construct a triangle of area equal to the area of this rhombus and one of the angles is 45°.

Important Questions on Construction-Drawing of Triangles Equal to the Area of a Given Quadrilateral

Learn and Prepare for any exam you want !

Construct a rhombus each side of which is $4 cm$ and one of whose angles is $60 °$ . Then construct a triangle of area equal to the area of this rhombus and one of the angles is $45 °$ .