A scale drawing of a proposed trapezoidal landscape design is shown in the figure below, with the given dimensions in meters. The trapezoid consists of a right triangle and a square divided into 3 isosceles right triangles. The unshaded regions will be white rock; the shaded triangular regions will be black rock. What is the area, in square meters, that will be black rock?

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We can find the area of the triangle with base 14 and height 10:

$$ A = \frac{1}{2}bh $$ $$ A = \frac{1}{2}(14)(10) $$ $$ A = 70 $$

We need to subtract the smaller isosceles right triangle to get just the shaded region. The smaller isosceles right triangle is a quarter of the area of the square.

$$ A_{\text{shaded}} = 70 - \frac{1}{4}A_{\text{square}} $$ $$ A_{\text{shaded}} = 70 - \frac{1}{4}(10)^2 $$ $$ = 70-25 =\boxed{45} $$