A composite figure has three congruent triangles removed from it.

A square and a rectangle. The square is 8 feet by 8 feet, and the rectangle is 16 feet by 8 feet. 3 triangles are cut out of the figure. The triangles have a base of 8 feet and height of 8 feet.
What is the area of the shaded region?
96 feet squared
128 feet squared
160 feet squared
192 feet squared

step-by-step explanation:

given that there are two triangles j'k'l' and jkl>

the former is got by dilating the second one.

when drawn on a grid, (graph paper) coordinates of vertices of first triangle is

(6,12)j, (9,6)k and (12,9)l

side jk has length = distance between j and k

=

side j'k'=distance between j' and k'

=

ie j'k'l' has sides 1/3 of that of corresponding sides of jkl.

hence scale factor of 1/3 is used to get j'k'l'from jkl

where is the diagram? shown below where? ?

step-by-step explanation:

take the logarithm of both sides (the base of the log doesn't matter):

apply the exponent property - this says that :

distribute the log terms on both sides:

group like terms together:

divide through both sides by the coefficient on :

you can do some additional rewriting here using the properties of the logarithm to simplify things if you like: