Question

Find the area of ABCDE where BC = 5 cm, CD = 18 cm, DE = 14 cm and AE = 6 cm.

Answer 1

To find the area of pentagon ABCDE, we can divide it into two shapes:

1. Trapezium ABCE
2. Rectangle CDEB

Step 1: Analyze the Shape

From the image and given values:

• AE = 6 cm
• DE = 14 cm
• CD = 18 cm
• BC = 5 cm

Draw a perpendicular from A to CD, call the foot of the perpendicular F.

Then:

EF = DE = 14 cm   ...(Height of rectangle)

AF = BC = 5 cm   ...(Height of trapezium)

CE = CD – AE   ...(Length of base of trapezium ABCE)

= 18 – 6

= 12 cm 

Step 2: Area Calculations

Rectangle CDEF:

Length = AE = 6 cm

Breadth = DE = 14 cm

Area_rect = 1 × b

= 6 × 14

= 84 cm²

Trapezium ABCE:

Parallel sides: AB = assume same as CD – AE = 12 cm and AE = 6 cm

Height = BC = 5 cm

`"Area"_("trap") = 1/2 xx (AB + CE) xx h`

= `1/2 xx (6 + 12) xx 5`

= `1/2 xx 18 xx 5`

= 45 cm²

Total Area:

Total Area = Area of rectangle + Area of trapezium

= 84 + 144

= 198 cm²