Question

The area of the triangular​

Answer 1

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!

Answer 2

24
`cm^(2)`

Explanation:

a =
`(bh)/(2)`

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

`a^(2)` +
`b^(2)` =
`c^(2)`

`6^(2)` +
`b^(2)` =
`10^(2)`

36 +
`b^(2)` = 100 Subtract 36 from both sides

`b^(2)` = 64

`\sqrt{b^(2) }` =
`√(64)`

b = 8

a =
`(bh)/(2)`

a =
`(6x8)/(2)` =
`(48)/(2)` = 24