The area of the house drawing given in the figure is ____.

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Firstly we will calculate the area of the triangle.
It is given that two sides of the triangle are of length 5cm and the third side is of length 6cm.

Area of triangle = \frac{1}{2} \times Base \times Height

where, base is equal to 6cm and height we have to calculate.
So when we draw a perpendicular on the base it will divide it into two parts each of 3cm length. So by applying Pythagoras theorem we will get the height of the triangle. Therefore,
Height of the triangle =

\sqrt{5^{2} - 3^{2}}

=

\sqrt{25 - 9}

=

\sqrt{16}

= 4cm
Therefore, area of triangle =

\frac{1}{2} \times 6 \times 4 = 12 c m^{2}

It is given that the total height of the house is 10cm and we found that the height of the triangle is 4 cm. So by subtracting the height of the triangle from the total height of the house, we will get the remaining height of the lower portion of the house.
Height of the lower portion of the house =10−4 = 6 cm
Now we will find the area of the square below the triangle.
Area of the square = side2 where, side is equal to 6 cm
Therefore, area of the square = 6×6 = 36 cm2
Now we will calculate the area of the rectangle which is to the right of the square.
Area of the rectangle = Base × Height where, base is equal to 8cm and height is equal to 6cm as height of the rectangle is equal to the remaining height of the house.
Therefore, area of the rectangle =8×6 = 48 cm2
Now we will calculate the area of the parallelogram.
Area of the parallelogram = Base × Height where, base is equal to 8cm and height is equal to 4cm as height of the triangle is equal to the perpendicular height of the parallelogram.
Therefore, area of the parallelogram =8×4 = 32cm2
Now by adding all the areas we will get the value of the total area of the house given in the figure.
Therefore, total area of the house =12+36+48+32 = 128cm2
Hence, 128cm2 is the total area of the house.

The area of the house drawing given in the figure is ____.

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