Question

In the diagram, PQRS is a trapezium with PS = x, SR =x+ 1, RQ=x+ 6 and

PQ=x-1
Also
(a) Give an expression, in terms of x, for the area of the trapezium. Show that it simplifies to x^2+ 2x-3.

(b) The area of the trapezium is 96 cm. Write an equation for the area, and solve for x.

(c) Calculate the perimeter of the trapezium.

Answer 1

a. The expression for the area of the trapezium simplifies to
`x^2`.

b. The value of x is 9.80

c. The perimeter of the trapezium is 45.19.

How to find perimeter of trapezium

(a) The expression for the area of a trapezium is given by:

Area = (1/2) * (sum of parallel sides) * (height)

In this case, the sum of the parallel sides is PQ + SR, which is (x-1) + (x+1) = 2x. The height of the trapezium is PS, which is x.

Substituting these values into the area formula:

Area = (1/2) * 2x * x =
`x^2`

So the expression for the area of the trapezium simplifies to
`x^2`.

(b) Since the expression for the area is
`x^2`, set up the equation:

`x^2` = 96

To solve for x, take the square root of both sides:

x = √96

x = 9.80

Therefore, x is equal to 9.80.

(c) To calculate the perimeter of the trapezium, add up the lengths of all four sides.

Perimeter = PQ + QR + RS + SP

PQ = x - 1

QR = x + 6

RS = x + 1

SP = x

Adding these lengths together:

Perimeter = (x - 1) + (x + 6) + (x + 1) + x

= 4x + 6

So the perimeter of the trapezium is 4x + 6.

since x = 9.80

Perimeter = 4( 9.80) + 6

Perimeter = 4(9.80) + 6

Perimeter = 39.19 + 6

Perimeter = 45.19

Therefore, the perimeter of the trapezium is 45.19.