What is the area of a 45-45-90 triangle, with a hypotenuse of 8mm in length?

Answer 1

#4mm^2#

The formula for calculating the area of a triangle is #1/2base*height#.

Thanks to the fact that this is a 45-45-90 triangle the base of the triangle and the height of the triangle are equal. So we simply need to find the values of the two sides and plug them into the formula.

We have the length of the hypotenuse, so we can use the pythagorean theorem to calculate the length of the two sides.

(we know the area is going to be measured in #mm^2# so we'll leave units out of the equations for now)

#a^2 + b^2 = 8^2#

#a=b#

We can simplify here, because we know the two remaining sides are equal. So we're just going to solve for

#a^4 = 16#
#a^2 = 8#
#a = sqrt(8)#

Both non-hypotenuse sides of the triangle are #sqrt(8mm)# long. Now we can use the triangle area formula so solve.

#area = 1/2base * height = 1/2 * sqrt(8) * sqrt(8) = 1/2 * 8 = 4mm^2#

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Answer 2

The area of a 45-45-90 triangle can be calculated using the formula A = (1/2) * leg^2, where leg represents the length of one of the legs of the triangle. In a 45-45-90 triangle, the legs are congruent, so if the hypotenuse has a length of 8mm, each leg will have a length of 8 / √2 mm. Substituting this value into the formula, we get A = (1/2) * (8 / √2)^2. Simplifying, we find A = (1/2) * (64 / 2) = 16 square millimeters. Therefore, the area of the 45-45-90 triangle with a hypotenuse of 8mm is 16 square millimeters.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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