Question

Construct a trapezium DEAN in which DE is parallel to NA, DE = 7 cm, EA = 6.5 cm, $\angle$ EDN = 100${}^{\circ }$ and $\angle$ DEA = 70${}^{\circ }$ . Also find its area.

Answer 1

Given: DE=7 cm, EA = 6.5cm $\angle$ EDN = 100${}^{\circ }$ and $\angle$ DEA = 70${}^{\circ }$ and DE || NA.

Steps:

Step 1. Draw a line segment DE= 7 cm.

Step 2. Construct an angle $\angle$ DEX = 70${}^{\circ }$ at E.

Step 3. With E as centre draw an arc of radius 6.5cm cutting EX at A.

Step 4. Draw AY parallel to DE.

Step 5. Construct an angle $\angle$ EDZ = 100${}^{\circ }$ at D cutting AY at N.

Step 6. DEAN is the required trapezium.

By measuring the length of AN = 5.8 cm and Height of trapezium = 6.1 cm

Area of the trapezium DEAN $=\frac{1}{2}\times h\times (a+b)$ sq.units

$=\frac{1}{2}\times 6.1\times (7+5.8)=39.04$ sq.cm