Write the algebraic expression that represents the area of the given figure in square
We begin by noticing that the figure is split into two shapes, a square and a
triangle. We are asked to find an algebraic expression for the area of the figure. Recall that the area of a square can be calculated by squaring the side length,
written 𝑙 squared. Since the side length of the square in this question is 𝑥 centimeters, then its area
is 𝑥 squared square centimeters.
Next, we recall that the area of a triangle is equal to half the length of the base
multiplied by the perpendicular height. The base of the triangle is 34 centimeters. And since we have a right triangle, the perpendicular height is 𝑥 centimeters. This means that the area of the triangle is equal to 34 multiplied by 𝑥 divided by
two. This can be simplified to 34𝑥 over two, which is equal to 17𝑥.
We now have expressions for the area of both the square and the triangle. The total area will be equal to the sum of these expressions. We can therefore conclude that the algebraic expression that represents the area of
the given figure is 𝑥 squared plus 17𝑥 square centimeters.