How to find the area of an acute / obtuse triangle - High School Math

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Question

If triangle ABC has vertices (0, 0), (6, 0), and (2, 3) in the xy-plane, what is the area of ABC?

Answer

Sketching ABC in the xy-plane, as pictured here, we see that it has base 6 and height 3. Since the formula for the area of a triangle is 1/2 * base * height, the area of ABC is 1/2 * 6 * 3 = 9.

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Question

The height, , of triangle in the figure is one-fourth the length of . In terms of h, what is the area of triangle ?

Answer

If $\dpi{100} \small h=\frac{1}{4}$ * $\dpi{100} \small \overline{PQ}$ , then the length of $\dpi{100} \small \overline{PQ}$ must be $\dpi{100} \small 4h$ .

Using the formula for the area of a triangle ( $\frac{1}{2}bh$ ), with $\dpi{100} \small b=4h$ , the area of the triangle must be $2h^{2}$ .

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Question

Find the area of a triangle whose base is and whose height is .

Answer

This problem is solved using the geometric formula for the area of a triangle.

$A=\frac{1}{2}bh$

Convert feet to inches.

$\dpi{100} \frac{2ft}{1}\frac{12in}{1ft}=24in$

$A=\frac{1}{2}14in24in$

$A=168in^{2}$

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Question

What is the area of a triangle with a height of and a base of ?

Answer

When searching for the area of a triangle we are looking for the amount of the space enclosed by the triangle.

The equation for area of a triangle is

Plug the values for base and height into the equation yielding

$\frac{1}{2}(4)(7)=Area$

Then multiply the numbers together to arrive at the answer .

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