Answer:
Part 1
The drawing of the quadrilateral is included here
Part 2
The area of the quadrilateral is 60.5 unit²
Explanation:
Part 1
Please find attached the given drawing of the quadrilateral created with Microsoft Excel
Part 2
The given quadrilateral ABCD comprises of a trapezium AECD and triangle ABE
The height of the trapezium, h₁ = 4 units
For segment BC, we have;
The slope = (-5 - (-2))/(5 - (-4)) = -1/3
The equation of the line BC in point and slope form is y - (-5) = -1/3×(x - 5)
Which gives;
y = -1/3×(x - 5) - 5 = -x/3 + 5/3 - 5 = -x/3 - 10/3
The y-intercept is (0, -10/3)
The lengths of the opposite parallel sides of the trapezium AECD are;
a = 5 - (-2) = 7 and b = 7 - (-10/3) = 31/3
The area of the trapezium AECD = ((a + b)/2) × h₁ = ((7 + 31/3)/2) × 4 = 104/3 unit²
The height of triangle
The area of ABE, h₂ = 5
The base of triangle ABE = b = 31/3
The area of triangle ABE = 1/2 × b × h₂ = 1/2 × 31/3 × 5 = 155/6 unit²
The area of quadrilateral ABCD = The area of the trapezium AECD + The area of triangle ABE
∴ The area of quadrilateral ABCD = 104/3 unit² + 155/6 unit² = 60.5 unit².