a Let's find the area and perimeter one at the time.

Perimeter

To find the perimeter, we need to know the length of the shape's sides. We can find the length of the horizontal and vertical sides by counting the number of steps they span in those directions.

To find the last side we will add two segments, creating a right triangle.

To find the length of the last side we can use the Pythagorean Theorem.

a^{2} + b^{2} = c^{2}

SubstituteII

$a = 4$ , $b = 4$

4^{2} + 4^{2} = c^{2}

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Solve for

c

CalcPow

Calculate power

16 + 16 = c^{2}

SumToProdTwoTerms

$a + a = 2 a$

2 (16) = c^{2}

RearrangeEqn

Rearrange equation

c^{2} = 2 (16)

SqrtEqn

$LHS = RHS$

c = \pm 2 (16)

$c > 0$

c = 2 (16)

SqrtProd

$a \cdot b = a \cdot b$

c = 162

CalcRoot

Calculate root

c = 42

Let's include this final side in our diagram.

By adding the sides of the shape we can find the perimeter.

5 + 2 + 3 + 4 + 4 + 32 + 2 \approx 25.66 units

Area

To calculate the area we divide the shape into two rectangles and one triangle.

To calculate the triangle's area, we need its base and height. To calculate the rectangle's area we need their width and length. From the diagram we see that we know all of these dimensions, so we can find the shape's area by adding these products.

\frac{1}{2} (4) (4) + (5) (2) + (4) (4) = 34 units^{2}

Exercise

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