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The area of the rectangle shown below is 128 square units. Find the area of the inset triangle ABC

The area of the rectangle shown below is 128 square units. Find the area of the inset-example-1

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Answer: 64 square units

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Step-by-step explanation:

Recall these formulas

  • area of a triangle = 0.5*base*height
  • area of a rectangle = length*width

We can rewrite the second formula as

  • area of a rectangle = base*height

Which means the triangle is half the rectangle, when both share the same base and have the same height. The diagram shows this is the case with triangle ABC.

Therefore,

triangle ABC = 0.5*rectangle = 0.5*128 = 64 square units

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Another approach is to note the area of the rectangle in terms of x is:

area = length*width = x*(x+x) = x*2x = 2x^2

Then set this equal to 128 to solve for x.

Solving 2x^2 = 128 leads to x = 8 when x > 0.

The rectangle is 8 units tall and 16 units across.

area of triangle ABC = 0.5*base*height = 0.5*16*8 = 64 square units

User Christopher Grigg
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