Question

A child draws the figure of an aeroplane as shown. Here, the wings ABCD and FGHI are parallelograms, the tail DEF is an isosceles triangle, the cockpit CKI is a semicircle and CDFI is a square. In the given figure, BP ⊥ CD, HQ ⊥ FI and EL ⊥ DF. If CD = 8 cm, BP = HQ = 4 cm and DE = EF = 5 cm, find the area of the whole figure.

Answer 1

CD = 8 cm
BP = HQ = 4 cm
DE = EF = 5 cm
Area of the parallelogram ABCD = $B\times H$
$$\begin{gathered} =8\times 4 \\ =32\mathrm{sq}.\mathrm{cm} \end{gathered}$$

Area of parallelogram FGHI = $B\mathit{\times }H$
$$\begin{gathered} =8\times 4 \\ =32\mathrm{sq}.\mathrm{cm} \end{gathered}$$
Area of the square = ${\mathrm{Side}}^2$
=$8^2=64\mathrm{sq}.\mathrm{cm}$

In $∆$ELF, we have:
$$\begin{gathered} {\mathrm{EL}}^2=5^2-4^2 \\ {\mathrm{EL}}^2=9 \\ \mathrm{EL}=3\mathrm{cm} \end{gathered}$$

Area of $△$DEF = $\frac{1}{2}\times B\times H$
$$\begin{gathered} =\frac{1}{2}\times 8\times 3 \\ =12\mathrm{sq}.\mathrm{cm} \end{gathered}$$

Area of the semicircle =$\frac{1}{2}{\mathrm{\pi r}}^2$

$$\begin{gathered} =\frac{1}{2}\times \frac{22}{7}\times 16 \\ =25.12\mathrm{sq}.\mathrm{cm} \end{gathered}$$
∴ Total Area = Area of the parallelogram ABCD + Area of the parallelogram FGHI + Area of the triangle DEF + Area of the semicircle CKI + Area of the square
Total Area = 165.12 cm²