Exercise 129 Page 327

Practice makes perfect

a The area of a trapezoid is calculated by multiplying its height with the sum of its parallel sides, divided by 2.

A=1/2h(b_1+b_2) Let's identify these dimensions in the given trapezoid and then calculate the area.

To calculate the perimeter we need to find the last unknown side in the trapezoid, which we will call c. We can do this by using the Pythagorean Theorem. Let's label a few more sides that we are going to need.

To find y, we first have to find x by using the Pythagorean Theorem.

a^2+b^2=c^2

SubstituteValues

Substitute values

x^2+6^2=10^2

▼

Solve for x

CalcPow

Calculate power

x^2+36=100

SubEqn

LHS-36=RHS-36

x^2=64

SqrtEqn

sqrt(LHS)=sqrt(RHS)

x=± 8

x > 0

x= 8

Having found the value of x, we can also find y.

Now we can calculate the trapezoid's unknown side, again, by using the Pythagorean Theorem.

a^2+b^2=c^2

SubstituteValues

Substitute values

2^2+6^2=c^2

▼

Solve for c

CalcPow

Calculate power

4+36=c^2

AddTerms

Add terms

40=c^2

RearrangeEqn

Rearrange equation

c^2=40

SqrtEqn

sqrt(LHS)=sqrt(RHS)

c=± sqrt(40)

c > 0

c= sqrt(40)

When we know the unknown side of the trapezoid we can calculate the perimeter.

b To determine the shape's area we will divide it into a trapezoid and a rectangle, then identify the dimensions we need to calculate these shape's respective areas.

Since we know the length of the trapezoid's parallel sides and its height, we can calculate its area. Additionally, we know the rectangle's width and length so we can calculate its area as well. If we add these values we get the shape's total area.

To find the perimeter we also need to determine the shape's unknown side, which we can call x.

Now we can calculate the unknown side with the Pythagorean Theorem.

a^2+b^2=c^2

SubstituteValues

Substitute values

3^2+4^2=x^2

▼

Solve for x

CalcPow

Calculate power

9+16=x^2

AddTerms

Add terms

25=x^2

RearrangeEqn

Rearrange equation

x^2=25

SqrtEqn

sqrt(LHS)=sqrt(RHS)

x=± 5

x > 0

x= 5

When we know the shape's unknown side we can finally calculate the perimeter. Notice that the shape includes four sides that are 5 feet, three that are 2 feet, and one that is 4 feet.