Geometry

These are similar triangles so the sides of CDE are 1/3 of the sides of ADG. This makes the area of CDE 1/9 of the area of ADG, making ADG 9 x 42 = 378

1. We are given the area of the top triangle as 42. Use the Area of a triagle formula to determine the Base and Height.

A = 1/2 of the base x the height (A = 1/2 bh)

42 =1/2 base x height

42 x 2 = 1/ 2 x 2 x base x height

84 = base x height

84 = 12 x 7

Next, use the Pythagorean theorum to solve for the hypotenuse.

12 **2 + 7 **2 = c **2

Simplify this to 19.

The segments AB BC and CD are equal, and since you know them to be 19 a piece, you now have enough information to determine the lengths of the base and long side because the triangles are "similar" by a factor of three - 3. So you can multiply the sides by three to arrive at the larger scaled triangle.

7 * 3 = 21 (bottom / base)

AND


12 * 3 = 36 ( long side / height)



Now, plug this into the Area of a Triangle = 1/2 base x height.

Area = 1/2 x 21 * 36

Area of ADG is 378

Ferguson259 wrote: ↑

Wed Sep 19, 2018 1:16 am

Since you know AG = 3CE and DG = 3DE ...eq(1),

Now the area of the top most triangle(CDE)
=1/2(EC x DE) = 42 ...eq(2) (given)

And Now, consider the area of the entire triangle(ADG) = 1/2(AG x DG)
= 1/2(3EC x 3DE)-------- replace the values using (eq(1))
= 9/2(EC x DE)
= 9(1/2(EC x DE)) ---eq(3)--- in this 1/2(EC x DE) is equal to 42(given) i.e. eq(2) replace it in the eq(3) with the value 42.
= 9 (42) = 378.

I hope this is helpful.

thank you very much for taking out your time and helping with this