Question

Question 3
Radha made a picture of an aero plane with colored 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=11cm/2=5.5cm
Area of triangle
= √[s(s−a)(s−b)(s−c)]
=√[5.5(5.5−5)(5.5−5)(5.5−1)]cm²
=√[(5.5)(0.5)(0.5)(4.5)] 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.
(Divide the trapezium into a triangle and parallelogram)
Perpendicular height of parallelogram=(√1²−(0.5)²)cm
=√0.75 cm=0.866 cm
Area of trapezium = Area of parallelogram +Area of equilateral triangle

=(0.866)1+√3/4(1)²=0.866+0.433=1.299 cm²

Area of triangle(IV) =Area of triangle in (V)
=(12×1.5×6)cm²=4.5cm²
Total area of the paper used = 2.488+6.5+1.299+4.5×2
=19.287 cm²