Answer:
a) 93 cm²
b) 98 cm²
Explanation:
You want the areas of the squares shown in each of the figures.
Pythagorean theorem
The Pythagorean theorem tells you the square of the hypotenuse is the sum of the squares of the other two sides of a right triangle.
a)
The square of the hypotenuse is 17² = 289.
The sum of the squares of the other two sides is ...
shaded square + (14)² = 17²
shaded square + 196 = 289
shaded square = 289 -196 = 93 . . . . cm²
Sabcd = 93 cm².
b)
The square of the diagonal is the sum of the squares of the sides. Each of those squares is the area of interest:
14² = (shaded square) + (shaded square)
196 = 2(shaded square)
98 = shaded square
Sabcd = 98 cm².
__
Additional comment
Perhaps you have seen the attached figure. It is intended to show the squares on each of the legs of the right triangle, and to illustrate that the sum of the areas of the green and purple squares is the area of the red square. This figure compares to the one for part (a) of the problem.
a² +b² = c² ⇒ a² = c² -b²