# AREA AND PERIMETER WITH POLYNOMIALS WORKSHEET

Problem 1 :

Find, in simplest form, an expression for the perimeter P of: Problem 2 : Problem 3 : Find, in simplest form, an expression for the area A of:

Problem 4 : Problem 5 : Problem 6 :   The given triangle is a isosceles triangle. Side lengths of the given triangle are x + 3, x + 3 and x.

Perimeter of the triangle given = x + 3 + x + 3 + x

= 3x + 6

So, perimeter of the triangle is 3x + 6. The given figure is a rectangle.

Perimeter of rectangle = 2(length + width)

Length = 3x - 4 and width = x + 1

= 2(3x - 4 + x + 1)

= 2(4x - 3)

= 8x - 6

So, the required perimeter is 8x - 6. Perimeter of the shape = 2(2x + 5) + 3(x - 2)

= 4x + 10 + 3x - 6

= 7x + 4 The given shape is rectangle.

Area of rectangle = length x width

length = x + 1 and width = 3x

= (x + 1) ⋅ 3x

= 3x+ 3x Area of triangle = (1/2) ⋅ base ⋅ height

1/2 ⋅ (x + 4) ⋅ 3

= (3/2)(x + 4) Area of given shape = Area of square + Area of triangle

Side length of square = x + 2, base of triangle = x + 2 and height of the triangle = x.

Area of square = (x + 2)(x + 2)

= x+ 4x + 4

Area of triangle = (1/2) ⋅ base ⋅ height

= (1/2) ⋅ (x + 2) ⋅ x

= x(x + 2)/2

Area of the shape = (x+ 4x + 4) + x(x + 2)/2

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