Question

Find the area of the trapezoid to the nearest tenth.

Answer 1

Answer:

2.2 metres squared

Step-by-step explanation:

We need to find the area of this trapezoid.

The area of a trapezoid is denoted by:

$A=\frac{(b_1+b_2)h}{2}$, where $b_1$ and $b_2$ are the parallel bases and h is the height

Here, we already know the lengths of the two bases; they are 0.9 metres and 2.3 metres. However, we need to find the length of the height.

Notice that one of the angles is marked 45 degrees. Let's draw a perpendicular line from top endpoint of the segment labelled 0.9 to the side labelled 2.3. We now have a 45-45-90 triangle with hypotenuse 2.0 metres. As one of such a triangle's properties, we can divide 2.0 by √2 to get the length of both legs:

2.0 ÷ √2 = √2 ≈ 1.414 ≈ 1.4

Thus, the height is h = 1.4 metres. Now plug all these values we know into the equation to find the area:

$A=\frac{(b_1+b_2)h}{2}$

$A=\frac{(0.9+2.3)*1.4}{2}=2.2$

The answer is thus 2.2 metres squared.

~ an aesthetics lover