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

Write an expression for the area of the trapezium below. Expand any brackets and fully-example-1
User Jomafer
by
8.8k points

2 Answers

7 votes

Answer:

.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

User Arthur Klezovich
by
8.1k points
3 votes

Answer:


\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:


\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:


\sf 24r^2 +46r + 21

User Vinod Bhatt
by
8.3k points

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