express the area of each triangle as a monomial.
10. height-2n^2
base- 5n^3
11. height- 4ab^5
base- 3a^4b
area = (1/2) base*height
10. (1/2)(5 n^3)(2 n^2)
to multiply, add exponents
5 n^(3+2)
or
5 n^5
11. (1/2) (3 a^4 b^1)(4 a^1 b^5)
6 a^(4+1) b^(1+5)
or
6 a^5 b^6
yes but in the first one (#10) the 1/2 and the 2 is not included. I don't know what to do with that.
Oh, do the arithmetic separately
(1/2)(5) (2) = 5
In the second one it is
(1/2)(3)(4)
you could say that is
(1.5)(4)
or
6
but I looked at it and said to myself ---half of four is two, so it is two times three or 6
To find the area of a triangle, you can use the formula: A = (1/2) * base * height.
Let's apply this formula to the given triangles:
10. Triangle with height = 2n^2 and base = 5n^3:
A = (1/2) * 5n^3 * 2n^2
= 5/2 * n^3 * n^2
= 5/2 * n^(3+2)
= 5/2 * n^5
= 2.5n^5
Therefore, the area of the triangle with height 2n^2 and base 5n^3 is expressed as the monomial 2.5n^5.
11. Triangle with height = 4ab^5 and base = 3a^4b:
A = (1/2) * 3a^4b * 4ab^5
= 6a^4b * ab^5
= 6a^5b^(1+5)
= 6a^(4+1)b^6
= 6a^5b^6
Hence, the area of the triangle with height 4ab^5 and base 3a^4b is represented as the monomial 6a^5b^6.