Respuesta :

Answer:

24 [tex]cm^{2}[/tex]

Step-by-step explanation:

a = [tex]\frac{bh}{2}[/tex]

We have the base, we need the height.  Use the Pythagorean Theorem

[tex]a^{2}[/tex] + [tex]b^{2}[/tex] = [tex]c^{2}[/tex]

[tex]6^{2}[/tex] + [tex]b^{2}[/tex] = [tex]10^{2}[/tex]

36 + [tex]b^{2}[/tex] = 100  Subtract 36 from both sides

[tex]b^{2}[/tex] = 64

[tex]\sqrt{b^{2} }[/tex] = [tex]\sqrt{64}[/tex]

b = 8

a = [tex]\frac{bh}{2}[/tex]

a =[tex]\frac{6x8}{2}[/tex] =[tex]\frac{48}{2}[/tex] = 24
Answer is area = 24 cm squared

Step by step

The area of a triangle is found using
1/2 base x height

Since we don’t know height, we need to find the third leg of this right triangle first

Using Pythagorean theorem a^2 + b^2 = c^2

c^2 is the hypotenuse (diagonal) and b^2 is the base so our unknown is a^2

a^2 + 6^2 = 10^2

a^2 + 36 = 100

Subtract 36 from both sides to isolate our unknown variable

a^2 + 36 - 36 = 100 - 36

a^2 = 64

Now take square root of both sides to solve for a

a = 8 (height)

Now we have a height of 8 and a base of 6

Our formula again is
A = 1/2 base x height

A = (1/2) (6) (8)

A = 24

Problem solved!



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