Area and perimeter problems

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Problem A01 A rectangle has a perimeter of 30 cm.

The width of the rectangle is 2 cm.

2 cm

Find the length of the rectangle.

Find the area of the rectangle.

Problem B01

A rectangle has a perimeter of 30 cm. The width of the rectangle is n cm.

The length of the rectangle is n+6 cm.

n

n+6

Write an expression for the perimeter in terms of n.

Write an equation and solve for n.

Area and perimeter problems

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Problem C01

A rectangle has an area of 40 cm2. The width of the rectangle is 5 cm.

5 cm

Find the length of the rectangle.

Find the perimeter of the rectangle.

Problem D01

A rectangle has an area of 40 cm2. The width of the rectangle is n cm.

The length of the rectangle is n+6 cm.

n

n+6

Write an expression for the area in terms of n.

Write an equation and solve for n.

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Problem A02 A rectangle has a perimeter of 24 cm.

The width of the rectangle is 5 cm.

5 cm

Find the length of the rectangle.

Find the area of the rectangle.

Problem B01

A rectangle has a perimeter of 24 cm. The width of the rectangle is n cm.

The length of the rectangle is n+1 cm.

n

n+1

Write an expression for the perimeter in terms of n.

Write an equation and solve for n.

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Problem C02

A rectangle has an area of 72 cm2. The width of the rectangle is 12 cm.

12 cm

Find the width of the rectangle.

Find the perimeter of the rectangle.

Problem D02

A rectangle has an area of 72 cm2. The width of the rectangle is n cm.

The length of the rectangle is n-14 cm.

n - 14

n

Write an expression for the area in terms of n.

Write an equation and solve for n.

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Problem E01 The perimeter of a regular pentagon is 90cm.

Find the length of each side of the pentagon.

A pentagon has a perimeter of 120cm; find the side length.

Problem B01

The perimeter of a regular pentagon is 90cm. Each side length is n+15.

n+15

Write an expression for the perimeter in terms of n.

Write an equation and solve for n.

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Problem F01 The perimeter of a regular hexagon is 480mm.

Find the length of each side of the hexagon.

A hexagon has a perimeter of 276m; find the side length.

Problem F02

The perimeter of a regular hexagon is 144cm. Each side length is n-5.

n-5

Write an expression for the perimeter in terms of n.

Write an equation and solve for n.

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Problem G01 The angles in a triangle are n+30 n+50 2n.

Write an equation and solve for n.

Work out the size of each angle in the triangle.

Problem G02

The angles in a triangle are n+35 2n+10 2n-5.

Write an equation and solve for n.

Work out the size of each angle in the triangle.

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Problem G03 The angles in a triangle are 4n-15 3n+45 n-10.

Write an equation and solve for n.

Work out the size of each angle in the triangle.

Problem G04

The angles in a triangle are 5n-18 2n+34 4n+43.

Write an equation and solve for n.

Work out the size of each angle in the triangle.

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Problem H01 The angles in a quadrilateral are

2n-10 n+13 4n+43 2n-28.

Write an equation and solve for n.

Work out the size of each angle in the quadrilateral.

Problem H02

The angles in a quadrilateral are 3n30 n+10 3n+40 3n+20.

Write an equation and solve for n.

Work out the size of each angle in the quadrilateral.

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Problem H03 The angles in a quadrilateral are

7n+24 80-2n 3n+91 100-3n.

Write an equation and solve for n.

Work out the size of each angle in the quadrilateral.

Problem H04

The angles in a quadrilateral are 2n-28 3n-7 2n-12 3n-23.

Write an equation and solve for n.

Work out the size of each angle in the quadrilateral.

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One star A number problem presented with a diagram.

One step to solve the problem.

A01 C01

A02 C02

E01 F01

Two stars A number problem presented with a diagram.

Two steps to solve the problem.

A01 C01

A02 C02

E01 F01

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Three stars Write expressions to represent the information.

Write and solve an equation,use solution for another problem.

Four stars A quadratic equation.

B01 B02 E02 F02

G01 G02 G03 G04

H01 H02 H03 H04

D01 D02

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How many stars?

More stars for

level of challenge number of challenges

Work together to solve more problems.

Resource title

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Solutions

Card

A01 13cm 26cm2

A02 7cm 35cm2

B01 4n+12 4n+12=30 n=4.5

B02 4n+2 4n+2=24 n=5.5

C01 8cm 26cm

C02 6cm 36cm

D01 n(n+6) n(n+6)=40 n2+6n-40=0 n=4 valid soln

D02 n(n-14) n(n-14)=72 n2-14n-72=0 n=18 valid soln

E01 18cm 24cm

E02 5(n+15) 5(n+15)=90 n=3

F01 80mm 46m

F02 6(n-5) 6(n-5)=144 n=29

G01 4n+80=180 n=25 55o, 75o, 50o

G02 5n+40=180 n=28 63o, 66o, 51o

G03 8n+20=180 n=20 65o, 105o, 10o

G04 11n+59=180 n=11 37o, 56o, 87o

H01 9n+18=360 n=38 66o, 51o, 195o, 48o

H02 10n+40=360 n=32 66o, 42o, 136o, 116o

H03 5n+295=360 n=13 115o, 54o, 130o, 61o

H04 10n70=360 n=43 58o, 122o, 74o, 106o