To find the area of X, we must first identify what values we are given, and how we can use these to solve the problem. We are given the length of the rectangle, 18cm, and its overall perimeter, 56cm. Simple geometry will assure us that from these two values, we can find the value of the side of the rectangle, 10, as on a rectangle both lengths are always the same, and (56-18x2)/2 = 10. Now, these lengths appear seemingly pointless, until we group the two triangles, the uppermost triangle and the triangle we are trying to determine the value of. Once we have done this, we are immediately given two dimensions of the triangle. Its height, 10, is equal to the overall height of the rectangle, and its length, 18, is equal to the overall length of the triangle. To determine the area of the triangle as a whole, we simply use the universal law used to determine the area of a triangle using its height and width, that of A= WxH/2. Once we know the total area of the triangle (10x18/2 = 90), we can simply remove the area of the uppermost original triangle we are given at the start, 42, to leave us with the area of x, 48. We have now solved the problem.
~Angus Lye
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