Question

Sara has designed the blades of a windmill, as shown in the diagram above. Find the total area covered by the blades of the windmill.

• A. 36 sq. in
• B. 120 sq. in
• C. 84 sq. in
• D. 96 sq. in

Answer 1

The correct option is B 120 sq. in

Here, mark the different shapes for a better understanding in the following way:


We observe that Figure I is a square while Figures II, III, IV & V are right triangles with the same dimensions.

So, the area of triangles II, III, IV & V, all will be equal.

$\text{Now, area of a square}={\text{Side}}^2$

$\text{So, area of Figure I is}=6^2=36\text{sq. in}$

$\text{Area of a triangle}=\frac{1}{2}\times \text{height}\times \text{base}$

Base of Figure II = 6 in
Height of Figure II = 7 in

So, area of the right-angled triangle in $\text{Figure II}=\frac{1}{2}\times 6\times 7=21\text{sq. in}$

∴ Area of Figure II = Area of Figure III = Area of Figure IV = Area of Figure V

Total area covered by the windmill =
Sum of areas of Figures I, II, III, IV and V
$=36+4\times 21=120\text{sq. in}$