The formula for the area of a triangle is A = 1/2 x b x height. But, we don't have the height here. To find the height, we can use the Pythagorean theorem.

With Pythagorean theorem, we'll be finding one of the legs. If we split the original triangle in 1/2 from the vertex to the base, we now have two right triangles. Both of these right triangles have a 30 cm hypotenuse and one 13 cm leg (remember we divided the entire original triangle in half).

30^2 = 13^2 + b^2

169 + b^2 = 900

b^2 = 731

b = $\sqrt{731}$

Now that we know the height of the triangle, we can find the area.

A = 1/2 x 26 x $\sqrt{731}$

A = 13 x $\sqrt{731}$

A = 351.48

The final area, rounded to the nearest whole number is 351 centimeters squared.

Note: Please know that depending on if the answer rounded $\sqrt{731}$ before using it to find the area, the final answer may then be rounded to 352.

Hope this helps! :)

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3 years ago