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QuestionFind the area of a triangle with base 545 cm5 \sqrt{45} \mathrm{~cm} and height 388 cm3 \sqrt{88} \mathrm{~cm}. Use A=12bhA=\frac{1}{2} bh.

Studdy Solution

STEP 1

Assumptions1. The base of the triangle is 545 cm5 \sqrt{45} \mathrm{~cm} . The height of the triangle is 388 cm3 \sqrt{88} \mathrm{~cm}
3. The formula for the area of a triangle is A=1bh\mathrm{A}=\frac{1}{} \mathrm{bh}, where b\mathrm{b} is the base and h\mathrm{h} is the height.

STEP 2

We need to find the area of the triangle. We can do this by substituting the given values of base and height into the formula for the area of a triangle.
A=12bh\mathrm{A}=\frac{1}{2} \mathrm{bh}

STEP 3

Now, plug in the given values for the base and height to calculate the area.
A=12×545×388\mathrm{A}=\frac{1}{2} \times5 \sqrt{45} \times3 \sqrt{88}

STEP 4

Rearrange the terms to simplify the calculation.
A=12××3×45×88\mathrm{A}=\frac{1}{2} \times \times3 \times \sqrt{45} \times \sqrt{88}

STEP 5

Calculate the numerical coefficient.
A=12×5×3=7.5\mathrm{A}=\frac{1}{2} \times5 \times3 =7.5

STEP 6

Combine the square roots under one radical.
A=.5×45×88\mathrm{A}=.5 \times \sqrt{45 \times88}

STEP 7

Calculate the value under the square root.
A=7.5×3960\mathrm{A}=7.5 \times \sqrt{3960}

STEP 8

implify the square root.
A=7.5×63\mathrm{A}=7.5 \times63

STEP 9

Calculate the area of the triangle.
A=7.5×63=472.5 cm2\mathrm{A}=7.5 \times63 =472.5 \mathrm{~cm}^2The area of the triangle is 472.5 cm2472.5 \mathrm{~cm}^2.

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