Video: Using Trigonometric Formula for Area of Triangle to Find the Area of a Triangle

Benjamin’s house is on a corner lot. Find the area of the front yard given that the edges measure 40 ft and 56 ft, as shown in the diagram.

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Video Transcript

Benjamin’s house is on a corner lot. Find the area of the front yard, given that the edges measure 40 feet and 56 feet as shown in the diagram.

Looking at the diagram, we can see that the yard is triangular and as well as being given that the lengths of two of the sides of the triangle, we’re also given the measure of the angle between them, 135 degrees. We need to find the area of this triangular yard. And as we haven’t been given any perpendicular height, we can’t use our trusty formula, half base times height, here. We have to use the more general formula which tells us that the area of any triangle is equal to half the product of two of its side lengths times the sine of the angle between those two sides.

Let’s apply this formula to the situation we have in our diagram. The two side lengths we have are 56 and 40 feet, and the measure of the angle between those two sides is 135 degrees. So our area is half the product of 56 and 40 times sin 135. Putting this into our calculator, we get an area of 791.959 dot dot dot. And of course, the units of this area are square feet as both lengths were given in feet. And to the nearest square foot, this is 792 square feet.

So the area of the front yard of Benjamin’s house is 792 square feet, to the nearest square foot.

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