Find the area of the trapezoid by decomposing it into other shapes.
a) 60 cm2
b) 69 cm2
c) 84 cm2
d) 99 cm2

99 cm^2

Step-by-step explanation:

Solution 1: Don't decompose and instead use the trapeziod area theorem. (b1+b2)/2 * h. Using this we plug in the two bases and get (23+10)/2 *6 -->

16.5*6=99cm2

Solution 2: You follow the rules and decompose the trapeziod. Split it into two triangles and a rectangle. The area of the triangle on the left is (b*h)/2 which is equal to (3*6)/2 which is 9 cm2. Spliting the trapeziod gives the rectangle dimensions of 10x6. 10*6= 60cm2. Finally we must find the area of the triangle on the right. The height is 6cm in the diagram and the base would be the full base of the trapeziod(20+3)-(10+3) --> 23-13=10. Using the area formula for the triangle gives us 10*6/2 = 30cm2. To find the full area we must add all the shapes up, 9+60+30 = 99cm2

(n^3 - n)

= n(n-1)(n+1)

since it is divisible by 3 and 2 ,because it is a multiple 3 consecutive number

if, n-1 is odd then n+1 is also odd, then it is a multiple of 9

but if, n-1 is even then n+1 is also even, then it is a multiple of 4

so, largest multiple = max(9*2, 4*3) = max(18, 12) = 18