Question

Construct the quadrilateral DEAR where DE = 4cm, EA = 5cm, AR = 4.5 cm, $\angle E={60}^{\circ },\angle A={90}^{\circ }$.
[5 marks]

Answer 1

Solution:
Given, DE = 4cm, EA = 5cm, AR = 4.5cm, $\angle E={60}^{\circ },\angle A={90}^{\circ }$.

To construct: A quadrilateral DEAR.

Steps of construction:

(a) Draw a line segment DE = 4cm. [1 mark]

(b) At point E, construct an angle of ${60}^{\circ }$. [1 mark]

(c) Taking radius 5 cm, draw an arc from point E which intersects at A. [1 mark]

(d) Construct $\angle A={90}^{\circ }$, draw an arc of radius 4.5 cm with centre A which intersects at R. [1.5 marks]

(e) Join RD. [0.5 mark]

It is the required quadrilateral DEAR.