How do you solve this problem? Eli is using a rectangular canvas for a school art project. The shaded triangles represent the sections Eli will paint.

Question

A rectangular canvass is 6 cm wide by 8 cm long. The non-shaded portion is 8 cm tall on the left edge and forms an isosceles triangle

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Answer 1 · 2018-05-08T17:00:29

Since the triangle is half the area of the rectangle, the shaded and non-shaded regions have equal areas, each #24\ text{cm}^2#.

Let's assume the question is, what are the areas of the shaded and non-shaded (white) regions?

The white triangle has a base of #8# and an altitude of #6# so an area of half the rectangle,

#A = 1/2 (8)(6) = 24 # square cm

The shaded region is the other half of the rectangle, so must also have area #24.#

Answer 2 · 2018-05-08T17:01:33

Can I add a second answer? Yes!

I can add a second answer but I can't delete it.

Let's see if I can say something different.

The common side #s# of the isosceles triangle satisfies

#4^2 + 6^2 = s^2#

#s^2=52#

The area #a# of triangle given three squared sides #A, B, C# satisfies

#16a^2 = 4AB-(C-A-B)^2#

Here for the white triangle we have #A=8^2=64, B=C=52#

#16a^2 = 4(64)(52)-64^2=64(208-64)=64(144)=16(2^2)(12^2)#

#a = 24#

This is obvious from #a=1/2 b h,# but it's nice to see the general case.