A large square of side length 10 contains a smaller square of side length 4, as shown in the diagram. The corresponding sides of the two squares are parallel. What percentage of the large square is shaded? We know that the big square has length 10, as it's given to us, and the small square has length 4. Or if we look at these heights, the heights of the two grey trapezoids combined, we know that it will be 6, because 10 minus 4 is 6. Then both trapezoids have the shorter parallel side of 4 and the longer parallel side along the big square of 10. So the area of the trapezoid we know is the base 1 plus base 2 divided by 2 times h. So then the combined area of the two trapezoids will be the average of the long and short bases times the total height of both trapezoids, and we can calculate that as 10 plus 4 over 2, which is 7, times 6, we know is 42. So our answer is D.

geometry

square

trapezoid

area calculation

shaded percentage