a) The area of a square with a side length of \(\displaystyle 2\)

To find the area of a square, square the side length: \(\displaystyle 2^{2}=4\)

b) The area of a square with a side length of \(\displaystyle 3\)

\(\displaystyle 3^{2}=9\)

c) The area of a circle with a radius of \(\displaystyle 2\)

To find the area of a circle, multiply the radius by \(\displaystyle 2\pi\).

\(\displaystyle 2\cdot2\pi=4\pi\approx12.56\) (Here, we rounded \(\displaystyle \pi\) to \(\displaystyle 3.14\), because an exact number isn't necessary to answer the question.)

Therefore (c) is larger than (b) which is larger than (a).

Since the interior angles of a triangle add up to \(\displaystyle 180\), each angle of an equilateral triangle is \(\displaystyle 60\) degrees.

Each of the interior angles of a square is \(\displaystyle 90\) degrees.

The interior angles of a pentagon add up to \(\displaystyle 540\), so each angle in a regular pentagon is \(\displaystyle 108\) degrees.

\(\displaystyle 60< 90< 108\)

Find the three volume by multiplying height by length by width:

a) \(\displaystyle 4\cdot4\cdot4=64\)

    Half of this volume is \(\displaystyle 32\).

b) \(\displaystyle 2\cdot4\cdot4=32\)

c) \(\displaystyle 2\cdot2\cdot2=8\)

Remember that we are only looking at half of the volume in a).

Therefore (a) and (b) are equal but (c) is not.

Area is calculated by multiplying the side lengths:

a) area of a rectangle with side lengths \(\displaystyle 5\) and \(\displaystyle 3\)

\(\displaystyle 5\cdot3=15\)

b) area of a rectangle with side lengths \(\displaystyle 3\) and \(\displaystyle 4\)

\(\displaystyle 3\cdot4=12\)

c) area of a square with side length \(\displaystyle 4\)

\(\displaystyle 4\cdot4=16\)

Therefore (b) is less than (a), which is less than (c).

To find the side length of a cube from its volume, find the cube root:

\(\displaystyle \sqrt[3]{64}=4\)

To find the side length of a square from its area, find the square root:

b) \(\displaystyle \sqrt{64}=8\)

c) \(\displaystyle \sqrt{36}=6\)

(a) is smaller than (c), which is smaller than (b)

First, we find the areas of a, b, and c.

\(\displaystyle a=\pi r^2=\pi (5)^2=25\pi\)

\(\displaystyle b=s^2=(5)^2=25\)

\(\displaystyle c=(l)(w)=(4)(6)=24\)

Now we put them in order of size.

\(\displaystyle a>b>c\)

First, find the perimeter of the shapes.

Since the area of \(\displaystyle a\) is \(\displaystyle 36\), its side length is \(\displaystyle 6\), giving it a perimeter of \(\displaystyle 24\).

The perimeter of \(\displaystyle b\) is \(\displaystyle \pi *d=12\pi\).

The perimeter of \(\displaystyle c\) is \(\displaystyle 5*6=30\).

Since \(\displaystyle \pi>3\), \(\displaystyle 12\pi>36\).

Therefore, \(\displaystyle a< c< b\).

First, find the lengths given.

Since the square in \(\displaystyle a\) has area \(\displaystyle 49\), the side length is \(\displaystyle 7\). \(\displaystyle (A_{square}=side^2)\)

All sides of a square have equal lengths, so \(\displaystyle b\) gives us a length of \(\displaystyle 28/4=7\).

The area of a circle is \(\displaystyle \pi r^2\), and diameter is \(\displaystyle 2r\). Since area is \(\displaystyle \frac{49\pi}{4}\), \(\displaystyle r=\frac{7}{2}\), giving us \(\displaystyle d=7\).

The three lengths are equal, so \(\displaystyle a=b=c\).

First, find the areas.

Since the perimeter of \(\displaystyle a\) is \(\displaystyle 44\), its side length is \(\displaystyle 11\), making the area \(\displaystyle 121\).

For triangles, \(\displaystyle A=\tfrac{1}{2}b*h\), so the area of \(\displaystyle b\) is \(\displaystyle 60\).

For \(\displaystyle c\), circumference is \(\displaystyle 2\pi r\), making \(\displaystyle r=12\), giving us an area of \(\displaystyle 144\pi\).

Putting them in order, we get \(\displaystyle c>a>b\).

Find the perimeters first.

\(\displaystyle a=6*(7)=42\)

\(\displaystyle b=4*(10)=40\)

\(\displaystyle c=3*(14)=42\)

Putting them in order of size:

\(\displaystyle a=c>b\)