A kite in the shape of a square with a diagonal 32 cm and an isosceles triangle of base 8 cm and sides 6 cm each is to be made of three different shades as shown in Fig. 12.17. How much paper of each shade has been used in it?

Question

Infinity Learn · Accepted Answer

We know that, Heron's formulaArea of triangle $$=$$ s (s$$ $$-$$ $$a) (s$$ $$-$$ $$b) (s$$ $$-c)where$$, s is the $$semi-perimeter$$ $$=$$ half of the perimeterand  a, b and c are the sides of the triangle Given that, A kite in the shape of a square with a diagonal $$32$$ cmGiven diagonal BD $$=$$ AC $$=$$ $$32$$ cm, then OA $$=$$ $$1/2$$ AC $$=$$ $$16$$ cm.So square ABCD is divided into two isoscales triangles ABD and CBD of base $$32$$ cm and height $$16$$ cm.Area of ∆ABD $$=$$ $$1/2$$  ×base × $$height=$$ $$(32$$ × $$16)/2=$$ $$256$$ $$cm2$$ Therefore, Area of ∆ABD $$=$$ Area of ∆CBD $$=$$ $$256$$ $$cm2Now$$, for ∆CEFSemi Perimeter $$=$$ s $$=$$ $$(a$$ $$+$$ b $$+c)/2s$$ $$=$$ $$(6$$ $$+$$ $$6$$ $$+$$ $$8)/2s$$ $$=$$ $$20/2s$$ $$=$$ $$10$$ cmBy using above formulaArea of ∆CEF $$=$$ s $$(s$$ $$-$$ $$a) (s$$ $$-$$ $$b) $$(s$$ $$-c)=$$ $$10(10$$ $$-$$ $$6)(10$$ $$-$$ $$6)(10$$ $$-$$ $$8)=$$ $$10$$ × $$4$$ × $$4$$ × $$2=$$ $$8$$ $$5=$$ $$8$$ × $$2.24=$$ $$17.92$$ $$cm2Hence$$ the area of the paper used to make region I $$=$$ $$256$$ $$cm2$$, region II $$=$$ $$256$$ $$cm2$$,region III $$=$$ $$17.92$$ $$cm2$$.

Q.

Unlock the Full Solution and Master the Concept