Question

ABCD is a trapezium with AB=10cm,AD=5cm,BC=4cm,and DC-7cm?Find the area of ABCD?

Answer 1

Answer:

ANSWER

Given:

AB

is parallel to

DC

, AB = 10 cm, BC = 5 cm, AC = 8 cm and CD = 6 cm.

Steps for construction:

Step 1 : Draw a rough diagram and mark the given measurements.

Step 2 : Draw a line segment AB = 10 cm.

Step 3 : With A and B as centres draw arcs of radii 8 cm and 5 cm respectively and let them cut at C.

Step 4 : Join

AC

and

BC

.

Step 5 : Draw

CX

parallel to

BA

.

Step 6 : With C as centre and radius 6 cm draw an arc cutting

CX

at D.

Step 7 : Join

AD

. ABCD is the required trapezium.

Step 8 : From C draw

CE

⊥

AB

and measure the length of CE. CE = h = 4 cm. AB = a = 10 cm, DC = b = 6 cm.

Calculation of area:

In the trapezium ABCD, a = 10 cm, b = 6 cm and h = 4 cm.

Area of the trapezium ABCD =

2

1

h(a+b)

=

2

1

(4)(10+6)

=

2

1

× 4 × 16

=32cm

2

solution