Question

Find the area of the triangle

Answer 1

The area of the triangle is:

`\Large\displaystyle\text{$\begin{aligned}A\triangle &= (21+7√(15))/(2)\\ \\A\triangle &\approx 24.055\\ \\\end{aligned}$}`

You can easily find the area of a triangle using the formula:

`\Large\displaystyle\text{$\begin{aligned}A\triangle = (bh)/(2)\end{aligned}$}`

Where h is the height of the triangle, and b the base.

Looking at the figure we can see that h = 7, but we need to discover the base, we know that the base is:

`\Large\displaystyle\text{$\begin{aligned}b = 3 + x\end{aligned}$}`

Where:

`\Large\displaystyle\text{$\begin{aligned}8^2 &= x^2 + 7^2\\ \\x^2 &= 8^2 - 7^2 \\ \\x^2 &= 64 - 49\\ \\x^2 &= 15\\ \\x &= √(15)\end{aligned}$}`

Therefore, our base length is:

`\Large\displaystyle\text{$\begin{aligned}b &= 3 + x\\ \\b &= 3 + √(15)\\ \\\end{aligned}$}`

Then we can just apply the formula for the area:

`\Large\displaystyle\text{$\begin{aligned}A\triangle &= ((3+√(15))\cdot 7)/(2)\\ \\A\triangle &= (21+7√(15))/(2)\\ \\A\triangle &\approx 24.055\\ \\\end{aligned}$}`

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