Question

. Sameer made a birthday card in the shape of a trapezium ABCD as shown in the figure with AB = BC
= 3.5 cm. He cut off a quadrant BFEC from point C and painted it with green colour and decorated the rest
with paper flowers. Find the area which he decorated with paper flowers.​

Answer 1

Area decorated with paper flowers is 6.125 cm²

Solution:

Given ABCD is a trapezium.

BFEC is a quadrant painted with green colour.

ABFDE is the area decorated with paper flowers.

AB = BC = 3.5 cm, DE = 2 cm

To find the area decorated with paper flowers:

Top base of the trapezium (AB) = 3.5 cm

Bottom base of the trapezium = 3.5 cm + 2 cm = 5.5 cm

Height of the trapezium (BC) = 3.5 cm

Area of the trapezium = $\frac{1}{2}\times\text{sum of the parallel sides}\times\text{height}$

                                    $=\frac{1}{2}\times(3.5+5.5)\times3.5$

Area of the trapezium = 15.75 cm²

Radius of the quadrant (BC) = 3.5 cm

Area of the quadrant = $\frac{1}{4} \times \pi r^2$

                                   $=\frac{1}{4} \times \frac{22}{7} \times (3.5)^2$

Area of the quadrant = 9.625 cm²

Area decorated with paper flowers

                            = Area of the trapezium – Area of the quadrant

                            = 15.75 cm² – 9.625 cm²

                            = 6.125 cm²

Area decorated with paper flowers is 6.125 cm².