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Klio2033 [76]
3 years ago
5

Find the area of the irregular figure. Round to the nearest hundredth.

Mathematics
1 answer:
RSB [31]3 years ago
7 0

Answer:

67.5\text{ [square units]}

Step-by-step explanation:

The composite figure consists of one rectangle and two triangles. We can add up the area of these individual shapes to find the total area of the irregular figure.

<u>Formulas</u>:

  • Area of rectangle with base b and height h: A=bh
  • Area of triangle with base b and height h: A=\frac{1}{2}bh

By definition, the base and height must intersect at a 90 degree angle.

The rectangle has a base of 10 and a height of 5. Therefore, its area is A=10\cdot 5=50.

The smaller triangle to the left of the rectangle has a base of 2 and a height of 5. Therefore, its area is A=\frac{1}{2}\cdot 2\cdot 5=5.

Finally, the larger triangle on top of the rectangle has a base of 5 and a height of 5. Therefore, its area is A=\frac{1}{2}\cdot 5\cdot 5=12.5.

Thus, the area of the total irregular figure is:

50+5+12.5=\boxed{67.5\text{ [square units]}}

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Answer:

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Step-by-step explanation:

This is a solve the system question. Call H the height of the triangle and B the base. The question tells us:

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and

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Sub the first equation into the second (as H is already isolated). You will end up with a quadratic equation - solve that any way you wish (e.g. quadratic formula). I've provided the factored form below which shows you the roots:

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In this question, we take B=4. You can't have a negative side length so the other answer is eliminated. Now sub the value for B into either of the original equations. I'll use the first, again because H is already isolated:

H=2(4)-3\\H=8-3\\H=5

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