Question

Radha made a picture of an aeroplane with coloured papers as shown in the given figure. Find the total area of the paper used.

Answer 1

For triangle I

This triangle is an isosceles triangle.

Perimeter = 2s = (5 + 5 + 1) cm = 11cm

s = 11/2 = 5.5 cm

`"Area of triangle "=sqrt(s(s-a)(s-b)(s-c))`

                          `=[sqrt(5.5(5.5-5)(5.5-5)(5.5-1))]cm^2`

                          `=[sqrt((5.5)(0.5)(0.5)(4.5))]cm^2`

                          `=0.75sqrt11cm^2`

                           = (0.75 x 3.317) cm²

                           = 2.488 cm²  (Approximately)

 

For quadrilateral II

This quadrilateral is a rectangle.

Area = l × b = (6.5 × 1) cm² = 6.5 cm²

 

For quadrilateral III

This quadrilateral is a trapezium.

`"Perpendicular height of parallelogram "=(sqrt(1^2-(0.5)^2))cm = sqrt0.75 cm = 0.866 cm`

Area = Area of parallelogram + Area of equilateral triangle

`=(0.866)1+sqrt3/4(1)^2`

= 0.866 + 0.433

= 1.299 cm²

Area of triangle (IV) = Area of triangle in (V)

`=(1/2xx1.5xx6)cm^2`

= 4.5 cm²

Total area of the paper used = 2.488 + 6.5 + 1.299 + 4.5 × 2

= 19.287 cm²