In rectangle ACDE, AB=5cm, C=10cm, and BE=13cm (triangle within the rectange is BDE). What is the total area outside the triangle?

Answer 1

Assuming that (i) there is a point B between A and C along one side of the rectangle, and that (ii) you mean "BC=10cm" instead of "C=10cm", then it seems to me you have a right-angled triangle ABE with the hypoteneuse BE which has length 13cm, and length AB = 5cm, so the other side AE has length 12cm (=sqrt(13^2 - 5^2) by Pythagoras). B lies between A and C, and AB=5cm and BC=10cm, so the complete length is AC=15cm. The length of the other side of the rectangle (i.e. AE) is 12cm, so the area of the rectangle is 12cm x 15cm = 180cm^2. The area of the right-angled triangle is half the base times the height, which is 5cm * 12cm / 2 = 30cm^2. So the total area outside the triangle is (180-30) = 150cm^2.