Answer:
Step-by-step explanation:
23. Perimeter is the sum of all four sides: 2(10x^2) + 2(7xy^2) = 20x^2 + 14xy^2 This can also be written as 2x(10x + 7y^2)
The area is the base x the height. (7xy^2)*(10x^2) = 70x^3y^2
24. Perimeter is the sum of all sides:
(2a^3b) + (4ab) + (6a^3b)
Triangle area is (1/2)BH = (1/2)*(4ab)*(2a^3b) = 4a^43b^4
25. Area = (a + b) * h / 2, where a and b are the top and bottom sides.
A = (4xy + 8xy)*(3x^2/2)
A = 12xy*((3/2)x^2
A = 18x^3y
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Although it is not asked, the Perimeter of this trapezoid might be calculated as follows:
Perimeter = The challenge here is that the two legs of the trapezoid are not known. It appears to be an isocelles trapezoid, so that both legs would have equal length. I'll set z as the leg length. Perimeter would be 4xy + 8xy + 2z.
We can use the pythagorean theorm to calculate the hypotenuse. z, of the triangle on the right. The base is (8xy-4xy)/2 or 2xy.
(3x^2)^2 + (2xy)^2 = z^2
9x^4 + 4x^2y^2 = z^2
z^2 = 9x^4 + 4x^2y^2
z = (9x^4 + 4x^2y^2)^(1/2)
I can't find a solution to this formula that doesn't involve i, so I'll leave it as is.
Perimeter(P) = 4xy + 8xy + 2z
P = 4xy + 8xy + 2*((9x^4 + 4x^2y^2)^(1/2)) Ugly, so I know why the perimeter is not requested. (It looked like fun at the start.)
