
A child draws the figure of an aeroplane as given. Here the wings EDCF and AGHB are parallelograms, the tail ADK is an isosceles triangle, the cockpit BLC is a semicircle and the portion ABCD is a square. Let and . , , . The area of the figure is ,
(a)
(b)
(c)
(d)

Answer
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Hint: To find the total area of the aeroplane as per the drawing, we will find the area of parts in which the figure is divided such as, area of square, area of parallelogram, area of semicircle, and area of triangle. Then we will sum up all the areas and we will get the total area.
, , , .
Complete step-by-step answer:
In question it is given that a child draws an aeroplane which can be seen in figure below,
The plane is made by using different shapes such as, square, triangle, parallelogram and semi-circle. And we are asked to find the total area of the figure. So, to find total area we will divide the figure in different shapes as per the figure itself and then we will find the areas such as,
………………..(i)
Where, s is semi perimeter of three sides and a, b and c are the sides of triangle
……………….(ii)
…………………(iii)
………………….(iv)
Now, first of all we will consider the parallelograms, EDCF and AGHB, so the area of parallelograms EDCF and AGHB using the expression (iii) can be given as,
Now, parallelograms EDCF and AGHB are same in size so, we can say that , so the expression can be written as,
Now, for parallelogram AGHB breadth is AB and altitude is HQ, and their values are and , on substituting these values we will get,
Now, on considering the triangle ADK, the area of triangle can be given by using the formula (i) which can be seen as,
Now, s can be given as, , where value of DK and AK is same as triangle is isosceles and AD is as it is also a side of square. So, on substituting these values in expression of s we will get,
Now, substituting these values of s in expression of triangle and substituting values of a, b and c, i.e. 6, 5, and 5 we will get,
Now, on considering square ABCD, area of square can be given as,
Now, the value of side AB is and in square all the sides are same so, the area of square will be,
Now, on considering semicircle BLC, area of semicircle can be given as,
Now, from the figure we can see that the radius of the semicircle is half the length of side BC, so the value of radius will be . So, on substituting this value of r in expression we will get,
No, total area is summation of all the areas which can be given as,
So, substituting all the values we will get,
Hence, the total area of figure is .
Option (c) is the correct answer.
Note: Students must know all the formulas which are used in this problem. Otherwise the answer will be incorrect. Also, area of triangle can be found out by drawing perpendicular bisector i.e. KM such that triangle KML and KMD will be right angle So, KM and MD will be 3cm. Using Pythagora's theorem, we can find length of KM which will be equal to 4. So, then we have two right angle triangles. So, using the formula , we can find the area of both triangles. On adding both areas we will get the same answer i.e. .
Complete step-by-step answer:
In question it is given that a child draws an aeroplane which can be seen in figure below,

The plane is made by using different shapes such as, square, triangle, parallelogram and semi-circle. And we are asked to find the total area of the figure. So, to find total area we will divide the figure in different shapes as per the figure itself and then we will find the areas such as,
Where, s is semi perimeter of three sides and a, b and c are the sides of triangle
Now, first of all we will consider the parallelograms, EDCF and AGHB, so the area of parallelograms EDCF and AGHB using the expression (iii) can be given as,
Now, parallelograms EDCF and AGHB are same in size so, we can say that
Now, for parallelogram AGHB breadth is AB and altitude is HQ, and their values are
Now, on considering the triangle ADK, the area of triangle can be given by using the formula (i) which can be seen as,
Now, s can be given as,
Now, substituting these values of s in expression of triangle and substituting values of a, b and c, i.e. 6, 5, and 5 we will get,
Now, on considering square ABCD, area of square can be given as,
Now, the value of side AB is
Now, on considering semicircle BLC, area of semicircle can be given as,
Now, from the figure we can see that the radius of the semicircle is half the length of side BC, so the value of radius will be
No, total area is summation of all the areas which can be given as,
So, substituting all the values we will get,
Hence, the total area of figure is
Option (c) is the correct answer.
Note: Students must know all the formulas which are used in this problem. Otherwise the answer will be incorrect. Also, area of triangle can be found out by drawing perpendicular bisector i.e. KM such that triangle KML and KMD will be right angle So, KM and MD will be 3cm. Using Pythagora's theorem, we can find length of KM which will be equal to 4. So, then we have two right angle triangles. So, using the formula
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