Question

Please answer this question: What is the area of this triangle?

Answer 1

Answer:

$6 units^2$

Step-by-step explanation:

The total area of the triangle is the area of the two smaller triangles added together.

We will use the equation of the area of the triangle as

$A=\frac{1}{2}bh$ - where b is the length of the base of the triangle, and h is the height of the triangle.

First, we can use the Pythagorean Theorem to find the base of the right hand side triangle.

The theorem states that:

$a^2+b^2=c^2$ - where c is the length of the hypotenuse, and a & b are the other side lengths.

$2^2+b^2=3^2\\4+b^2=9\\b^2=5\\b=\sqrt{5}$  

Now we can substitute in our values to determine the area of the right hand side triangle.

$A=\frac{1}{2}*\sqrt{5} *2=\sqrt{5}$

As the two triangles have a shared base, we can now subtract our one base length to get the other base.

This gives us the base of our left hand side triangle as:

$6-\sqrt{5}$

Now we can substitute this into our area equation, for the left hand side:

$A=\frac{1}{2}*(6-\sqrt{5})*2=(6-\sqrt{5}) = (6-\sqrt{5})$

Now we add our two separate areas to get the overall area:

$A=\sqrt{5}+6-\sqrt{5}=6$

Answer 2

Answer:

6unit²

you're welcome

Step-by-step explanation:

area= ½bh