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Square & Triangular Plots of Land

by Andrew
(New York)










































The diagram below displays three square plots of land. Plot A is 388 square miles, plot B is 153 square miles, and plot C is 61 square miles. How big is the triangular plot of land between A, B, and C?

Comments for Square & Triangular Plots of Land

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Apr 27, 2012
Area of a Triangle using Heron's Formula
by: Staff


Question:

by Andrew
(New York)


The diagram below displays three square plots of land. Plot A is 388 square miles, plot B is 153 square miles, and plot C is 61 square miles. How big is the triangular plot of land between A, B, and C?



Answer:


The area between three square plots of land is a triangle.

Open the following link to view a diagram.

(1) If your browser is Firefox, click the following link to VIEW the solution; or if your browser is Chrome, Internet Explorer, Opera, or Safari (2A) highlight and copy the link, then (2B) paste the link into your browser Address bar & press enter:

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http://www.solving-math-problems.com/images/triangle-area-between-three-square-plots-of-land.png


To answer your question, (1) compute the side sides of the triangle, and then (2) use Heron's Formula to calculate the area of the triangle.

(1) Compute the sides of the triangle.

Each one of the three sides of the triangle is equal to the side of one of the rectangular plots of land.

Open the following link to view a diagram of the areas of the square plots of land.

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http://www.solving-math-problems.com/images/areas-of-three-square-plots-of-land.png


Since each plot of land is a square, the every side of each plot of land is the square root of the area.

Plot A – each side a = √(388) = 19.6977 mi

Plot B – each side b = √(153) = 12.3693 mi

Plot C – each side c = √(61) = 7.81025 mi


Open the following link to view a diagram of the length of the sides of each square plot of land.

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http://www.solving-math-problems.com/images/sides-square-plots-of-land.png



Open the following link to view a diagram of the length of the sides of the triangular parcel of land in the center.

Use the Backspace key to return to this page

http://www.solving-math-problems.com/images/sides-center-triangle.png



(2) use Heron's Formula to calculate the area of the triangle.

Semiperimeter (1/2 the perimeter)

s = (a + b + c) / 2

s = (19.6977 + 12.3693 + 7.81025) / 2

s = (39.87725) / 2

s = 19.938625


Heron's Formula for the area of the triangle
A = √[s (s - a) (s - b) (s - c)]


A = √[19.938625 (19.938625 - 19.6977 ) (19.938625 - 12.3693) (19.938625 - 7.81025)]


A = √[19.938625 (0.240925) (7.569325) (12.128375)]


A = √[19.938625 (0.240925) (7.569325) (12.128375)]


A = √(440.9982258194147)


A = 20.9999577575626



>>> the final answer: Area = 21.0 mi²





Thanks for writing.

Staff
www.solving-math-problems.com



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