Exercise 52 Page 628

The given quadrilateral is regular. For regular quadrilaterals it is true that all sides are congruent and all angles are right. Therefore, we know that the quadrilateral is a square.

We know that the triangle's hypotenuse is 10 feet. We want to find the length of its sides. We will then use the Pythagorean Theorem and that the sides of the triangle are congruent. By the definition of congruence they have the same length. Let's call this length s.

a^2+b^2=c^2

SubstituteValues

Substitute values

s^2+s^2=10^2

SumToProdTwoTerms

a+a=2a

2(s^2)=10^2

CalcPow

Calculate power

2(s^2)=100

DivEqn

.LHS /2.=.RHS /2.

s^2=50

SqrtEqn

sqrt(LHS)=sqrt(RHS)

s=sqrt(50)

Note that when solving the equation we kept the principal root, because s represents the length of a side and therefore is a positive number. Let's use that s=sqrt(50) feet in the formula for the area of a square. A=s^2 ⇒ A=( sqrt(50) )^2=50 ft^2 The area of the square is 50 ft^2.