Answer:

Explanation:
Trapezoid: A trapezoid is a quadrilateral with one pair of parallel sides. The parallel sides are called the bases of the trapezoid, and the other two sides are called the legs.
Area of a trapezoid: The area of a trapezoid is equal to the average of the lengths of the bases times the height. The height is the perpendicular distance between the bases.
Formula:

where
- a is the length of the first base
- b is the length of the second base
- h is the height of the trapezoid
In this case:
- a = 7r + 6
- b = 5r + 8
- h= 4r + 3
Now,
Substitute the value in above formula:
![\begin{aligned}\textsf{Area}&\sf = (1)/(2)* ((7r+6)+(5r+8))* (4r+3) \\\\ &\sf \textsf{Open the bracket and solve} \\\\ &\sf = (1)/(2)* (7r+6+5r+8)* (4r+3)\\\\ &\sf =(1)/(2) * (12r+14)* (4r+3)\\\\ &\sf = (1)/(2) * 2(6r+7)* (4r+3) \\\\&\sf = 6r(4r+3)+7(4r+3) \\\\ &\sf = 24r^2 + 18r + 28r+21 \\\\&\sf = 24r^2 +46r + 21 \end{aligned}]()
Therefore, expression to find the area of trapezoid is:
