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Area of this trapezoid=area of the rectangle +  area of the triangle

1) We calculate the area of the rectangle
Area of a rectangle=base  x  height
Data:
Base=320 miles
height=207 miles

Area of this rectangle=(320 miles)(207 miles)=66240 miles².

2) we calculate the area of the triangle
Area of a triangle=(base x heigth)/2

Data:
Base=320 miles
height=???

we calculate the height by Pythagoras theorem:
hypotenuse²=leg₁²+leg₂²

Data:
hypotenuse=405 miles
leg₁=base=320 miles
lleg₂=height.

(405 miles)²=height² +(320 miles)²
164025 miles²=height²+102400 miles²
height²=164025 miles²-102400 miles²
heigth²=61625 miles²
heigth=√(61625 miles²)=248.24 miles

Area of this triangle=(320 miles x 248.24 miles)/2≈39719 miles²

3)We calculate the area of this trapezoid:
Area of Nevada=area of this rectangle + area of this triangle.
Area of Nevada=66240 miles² +39719 miles²≈105959 miles²


Answer: 105959 sq. mi

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