Question

Write an expression for the area of the trapezium below. Expand any brackets and fully simplify your answer. ​

Answer 1

.Area = (large base+small base)/2*height

A =(7r+6+5r+8)/2* 4r+3

A =(12r+14)/2*4r+3

A = (6r+7)(4r+3)

A = 24r²+18r+28r+21

A = 24r²+46r+21

Answer 2

`\sf \textsf{Expression for the area of trapezoid:} 24r^2 +46 r + 21`

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:

`\sf Area = (1)/(2) * (a + b) * h`

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:

Therefore, expression to find the area of trapezoid is:

`\sf 24r^2 +46r + 21`