Below is regular Pentagon \(\displaystyle PENTA\) with center \(\displaystyle C\), a segment drawn from \(\displaystyle C\) to each vertex - that is, each of its radii drawn.

A kite is a quadrilateral with two sets of congruent adjacent sides, with the common length of one pair differing from that of the other. A regular polygon has congruent sides, so \(\displaystyle \overline{EN} \cong \overline{EP}\); also, all radii of a regular polygon are congruent, so \(\displaystyle \overline{CP} \cong \overline{CN}\). It follows by definition that Quadrilateral \(\displaystyle CPEN\) is a kite.

A kite is a geometric shape that has two sets of equivalent adjacent sides.

Thus, the length of side \(\displaystyle b=a+5\).

Since, \(\displaystyle a=\) \(\displaystyle 7\), \(\displaystyle b\) must equal \(\displaystyle 7+5=12\).  

A kite is a geometric shape that has two sets of equivalent adjacent sides. In this kite the two adjacent sides which are congruent are those at the top of the kite and then likewise, the two that are connected at the bottom of the kite.

Thus, \(\displaystyle a\) must equal \(\displaystyle 7\). 

A kite is a geometric shape that has two sets of equivalent adjacent sides.

Therefore plug in the given information into the formula: 

\(\displaystyle perimeter=2(a+b)\), where \(\displaystyle a\) and \(\displaystyle b\) are the lengths of opposite sides of the kite and solve for \(\displaystyle b\). 

\(\displaystyle 48=2(9+b)\)

\(\displaystyle \frac{48}{2}=(9+b)\)

\(\displaystyle 24=9+b\)

\(\displaystyle b=24-9=15\)

A kite is a geometric shape that has two sets of equivalent adjacent sides.

Therefore plug in the given information into the formula: 

\(\displaystyle perimeter=2(a+b)\), where \(\displaystyle a\) and \(\displaystyle b\) are the lengths of opposite sides of the kite and solve for \(\displaystyle a\). 

\(\displaystyle 88=2(a+31)\)

\(\displaystyle a+31=\frac{88}{2}\)

\(\displaystyle a=44-31=13\)

A kite is a geometric shape that has two sets of equivalent adjacent sides.

Therefore plug in the given information into the formula: 

\(\displaystyle perimeter=2(a+b)\), where \(\displaystyle a\) and \(\displaystyle b\) are the lengths of opposite sides of the kite and solve for \(\displaystyle b\). 

\(\displaystyle 450=2(94+b)\)

\(\displaystyle \frac{450}{2}=94+b\)

\(\displaystyle 225=94+b\)

\(\displaystyle b=225-94=131\)

A kite is a geometric shape that has two sets of equivalent adjacent sides.

Therefore plug in the given information into the formula: \(\displaystyle perimeter=2(a+b)\), where \(\displaystyle a\) and \(\displaystyle b\) are the lengths of opposite sides of the kite and solve for \(\displaystyle b\).


\(\displaystyle 4.5=2(0.5+b)\)

\(\displaystyle 0.5+b=\frac{4.5}{2}=2.25\)

\(\displaystyle b=2.25-0.5=1.75\)

A kite is a geometric shape that has two sets of equivalent adjacent sides.

Therefore plug in the given information into the formula: \(\displaystyle perimeter=2(a+b)\), where \(\displaystyle a\) and \(\displaystyle b\) are the lengths of opposite sides of the kite and solve for \(\displaystyle a\). 

\(\displaystyle 43=2(a+16)\)

\(\displaystyle a+16=\frac{43}{2}\)

\(\displaystyle a+16=21.5\)

\(\displaystyle a=21.5-16=5.5\)

A kite is a geometric shape that has two sets of equivalent adjacent sides.

In this particular case the top sides that are connected at the top are congruent and the two sides that are connected at the bottom are congruent.

Thus, side \(\displaystyle b\) must equal \(\displaystyle 16\) inches. 

A kite is a geometric shape that has two sets of equivalent adjacent sides.

Therefore plug in the given information into the formula: 

\(\displaystyle perimeter=2(a+b)\), where \(\displaystyle a\) and \(\displaystyle b\) are the lengths of opposite sides of the kite and solve for \(\displaystyle b\). 

\(\displaystyle 26=2(9.5+b)\)

\(\displaystyle 9.5+b=\frac{26}{2}\)

\(\displaystyle 9.5+b=13\)

\(\displaystyle b=13-9.5=3.5\)