The diagram shows a 20 by 20 square . The points E, F and G are equally spaced on side BC. The points H, I, J, and K on side DA are placed so that the triangles BKE, EGF, FIG, and GHC are isosceles. Points L and M are midpoints of the sides AB and CD, respectively. Find the total area of the shaded regions.

Guest Nov 12, 2019

#3**+2 **

fudge I accidently reloaded my page 2 times already, meaning that I had to re do my explanation two times.

calculate KBE

Base:

20/4 = 5

Height:

20

5 * 20 = 100 / 2 = **50**

base of grey triangle is half of KBE, because BC is divided into 4 congruent parts, while LM, equal to BC, is divided into 8 parts.

So calculate grey triangle:

Base:

5/2 = 2.5

Height:

20 / 2 = 10

10 * 2.5 = 25/2 = **12.5**

Count number of grey triangles.** 8 triangles**

So 12.5 * 8 = **100**

CalculatorUser Nov 12, 2019

#4**+1 **

I get the same as CU with a little different reasoning

BE = (1/2) BC = 20/4 = 5

And the height of triangle BKE = 20

So...it's area = (1/2) (5) (20) = 50

The gray portion of this triangle has 1/2 the base and /2 the height of BKE

So its area = (1/2) (1/2) (50) =50/4

And we have 8 of these congruent gray areas....so....the total gray area = 8 (50/4) = 100 units^2

CPhill Nov 12, 2019