Answer:
0.7 m²
Explanation:
You want the area of a trapezoid with bases 0.5 m and 1.3 m, a base angle of 45°, and a slant height of 1.1 m.
Area formula
The area of the trapezoid is given by the formula ...
A = 1/2(b1 +b2)h
The figure tells us b1 and b2. We have to figure out what h is.
Height
There are a couple of ways to find the height.
1) Using trigonometry, we find the height of the trapezoid to be the side of a right triangle opposite the given 45° angle. That triangle has a hypotenuse of 1.1 m.
Sin = Opposite/Hypotenuse
Opposite = Hypotenuse · Sin
height = (1.1 m)sin(45°) ≈ 0.7778 m
2) The bottom corner angles are not marked in the figure. If we assume they are right angles, then the excess length of the right "base" is 1.3 -0.5 = 0.8 m. Taking that to be one leg of a 45°-45°-90° right triangle, the other leg (the height of the trapezoid) is also 0.8 m. The second attachment shows this approach.
Area calculation
The first attachment shows the area calculation using the trig approach to height. The computed area is 0.7 m² when rounded to 1 decimal place.
Using the second method of finding the area, we compute it to be 0.72 m², which also rounds to 0.7 m².
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Additional comment
There are more dimensions on the figure than necessary to compute its area. Fortunately, they are consistent with each other when length and area are rounded to 1 decimal place.
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