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A monomial is a type of polynomial, which is an algebraic expression having only a non-zero single term. Monomial consists of only a single term which makes it easy to do the operation of addition, subtraction and multiplication. It consists of either only one variable or one coefficient or product of a variable and a coefficient with exponents as whole numbers, which represent only one term, unlike binomial and trinomial, which consist of two and three terms respectively. It cannot have a variable in the denominator.

The area of a triangle (A) is half of the the product of its height and base. That is,

$\text{´¡°ù±ð²¹â€‰â¶Ä‰o´Ú â¶Ä‰t°ù¾±²¹²Ô²µ±ô±ð}\left(A\right)=\frac{1}{2}×\text{³ó±ð¾±²µ³ó³Ùײú²¹²õ±ð â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰}…\left(1\right)$

If the two terms have the same base (in this case x) and are to be multiplied together their indices are added.

In general:$x^m×x^n=x^{m+n}$

Substitute$4a$ as the height and $5a{b}^2$as the base in the equation (1) to get the area of the given triangle.

$Area\left(A\right)=\frac{1}{2}×\left(4a\right)×\left(5a{b}^2\right)$

Collect the like terms together.

$Area\left(A\right)=\frac{1}{2}×\left(4×5\right)×\left(a×a\right)×\left(b^2\right)$

Apply multiplication rule to simplify further.

width="195" height="113" role="math">AreaA=1220a1+1b2=1220a2b2=10a2b2

From the definition a monomial expression must contain only one non-zero term.

Note: Even though it contains two variables$a,b$and a constant 20, all those are considered as one single term by the definition of monomial.

Therefore the monomial expression for the area of the triangle with height $4a$and a base of$5a{b}^2$ is $10a^2{b}^2$.