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# A door is in the shape of a rectangle surmounted by a semicircle. If the width of the door is 4 units and the height of the door is 10.25 units, find the total area of the door.

Last updated date: 14th Jul 2024
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Hint: - Here we go through by first figure out the diagram what the question says then apply the formula of area of rectangle and the area of semicircle. And then add them together to find the total area of the door.

Hence the radius of the semicircle ‘r’ is $\dfrac{4}{2} = 2$ because the radius is half of the diameter.
First we find out the area of rectangular figure by the help of the formula of area of rectangle i.e. $l \times b$
Area of rectangular figure =$l \times b = 4 \times 10.25 = 41$sq. unit
Now we find out the area of semicircle that is surmounted on the rectangular part by the formula of area of semicircle i.e. $\dfrac{{\pi {r^2}}}{2}$
Area of semicircular figure=$\dfrac{{\pi {r^2}}}{2} = \dfrac{{22}}{7} \times \dfrac{1}{2} \times 2 \times 2 = 6.28$ sq. unit