Area Worksheet



Area Worksheet

1.Determine the area of an isosceles right triangle with the equal sides each measuring 10 cm in length.

2.Calculate the number of trees that can be planted in a rectangular field which is 32 m long and 30 m wide if each tree needs 4 m² to grow.

3. The area of a trapezium is 120 m², the height is 8 m, and the smaller base measures 10 m. What is the length of the other base?

4. Calculate the area of a parallelogram whose height is 2 cm and its base is 3 times its height.

5. What is the area of the shaded area in the figure if the area of the entire hexagon is 96 cm²?

[pic]

6. Calculate the area of a rhombus whose larger diagonal measures 10 cm and whose minor diagonal is half the length of the other.

7. Calculate the number of square tiles needed to cover a rectangular surface of 4 m by 3 m if the length of each side of the tiles is 10 cm.

8. The perimeter of an equilateral triangle is 0.9 dm and its height is 25.95 cm. Calculate the area of the triangle.

9A rectangular field has a length of 170 m and a width of 28 m. Calculate:

1The area of the field in hectares.

2The price to re-seed the field if each square meter costs $15.

Area Word Problems

1. A square garden with a side length of 150 m has a square swimming pool in the very centre with a side length of 25 m . Calculate the area of the garden.

2. A rectangular garden has dimensions of 30 m by 20 m and is divided in to 4 parts by two pathways that run perpendicular from its sides. One pathway has a width of 8 dm and the other, 7 dm. Calculate the total usable area of the garden.

3. Calculate the area of the quadrilateral that results from drawing lines between the midpoints of the sides of a rectangle whose base and height are 8 and 6 cm respectively.

4. A line connects the midpoint of BC (Point E), with Point D in the square ABCD shown below. Calculate the area of the acquired trapezium shape if the square has a side of 4 m.

[pic]

5. Calculate the amount of paint needed to paint the front of this building knowing that 0.5 kg of paint is needed per m2.

[pic]

6. A wooded area is in the shape of a a trapezium whose bases measure 128 m and 92 m and its height is 40 m. A 4 m wide walkway is constructed which runs perpendicular to the two bases. Calculate the area of the wooded area after the addition of the walkway.

Pythagorean Theorem Word Problems

1. A 10 m long ladder is leaning against a wall. The bottom of the ladder is 6 m from the base of where the wall meets the ground. At what height from the ground does the top of the ladder lean against the wall?

2. Determine the side of an equilateral triangle whose perimeter is equal to a square of side 12 cm. Are their areas equal?

3. Calculate the area of an equilateral triangle inscribed in a circle of radius 6 cm.

4. Determine the area of the square inscribed in a circle with a circumference of 18.84 cm.

5. A square with a side of 2 m has a circle inscribed in it and in turn this circle has a square inscribed in it. If this square also has a circle inscribed in it, what is the area between the last square and the last circle.

6. The perimeter of an isosceles trapezium is 110 m and the bases are 40 and 30 m in length. Calculate the length of the non-parallel sides of the trapezium and its area.

7. A regular hexagon of side 4 cm has a circle inscribed and another circumscribed around its shape. Find the area enclosed between these two concentric circles.

8A chord of 48 cm is 7 cm from the center of a circle. Calculate the area of the circle.

9. The legs of a right triangle inscribed in a circle measure 22.2 cm and 29.6 cm. Calculate the circumference and the area of the circle.

10. A central angle of 60° is plotted on a circle with a 4 cm radius. Calculate the area of the circular segment between the chord joining the ends of the two radii and its corresponding arc.

11. There is a rope running from the top of a flagpole to a hook in the ground. The flagpole is 12 meters high, and the hook is 9 meters from its base. How long is the rope?

Triangle Problems

1. Determine the area of an isosceles right triangle with the equal sides each measuring 10 cm in length.

2. The perimeter of an equilateral triangle is 0.9 dm and its height is 25.95 cm. Calculate the area of the triangle.

3. A 10 m long ladder is leaning against a wall. The bottom of the ladder is 6 m from where the wall meets the ground. At what height from the ground does the top of the ladder lean against the wall?

4. Determine the side of an equilateral triangle whose perimeter is equal to a square of side 12 cm. Are their areas equal?

5. Calculate the area of an equilateral triangle inscribed in a circle of radius 6 cm.

6. The legs of a right triangle inscribed in a circle measure 22.2 cm and 29.6 cm. Calculate the circumference and the area of the circle.

7. Given an equilateral triangle with a side of 6 cm, find the area of the circular sector determined by the circle circumscribed around the triangle and the radius passing through the vertices.

8. The hypotenuse of a right triangle measures 405.6 m and the projection of a leg on it is 60 m in length. Calculate:

1 The length of the legs (catheti).

2 The height of the triangle.

3The area of the triangle.

9. Calculate the sides of a triangle knowing that the projection of one of the legs on the hypotenuse is 6 cm and the height is [pic]cm.

Circle Problems

1. A circular fountain of 5 m radius lies alone in the centre of a circular park of 700 m radius. Calculate the total walking area available to pedestrians visiting the park.

2. Calculate the shaded area, knowing that the side of the outer square is 6 cm and the radius of the circle is 3 cm.

[pic]

3. .In a circular park with a radius of 250 m there are 7 lamps whose bases are circles with a radius of 1 m. The entire area of the park has grass with the exception of the bases for the lamps. Calculate the lawn area.

Square Problems

1. Calculate the area and perimeter of a square with a side of 5 cm.

2. A square garden with a side length of 150 m has a square swimming pool in the very center with a side length of 25 m. Calculate the area of the garden.

3. Find the length of the diagonal of a square with a side of 5 cm.

4. Determine the area of the square inscribed in a circle with a circumference of 18.84 cm.

5. A square with a side of 2 m has a circle inscribed in it and in turn this circle has a square inscribed in it. If this square also has a circle inscribed in it, what is the area between the last square and the last circle.

6. Calculate the area enclosed by the inscribed and circumscribed circles to a square with a diagonal of 8 m in length.

7. Calculate the shaded area, knowing that the side of the outer square is 6 cm and the radius of the circle is 3 cm.

[pic]

Rectangle Problems

1. Calculate the area and perimeter of a rectangle with a base of 10 cm and a height of 6 cm.

2. Calculate the number of trees that can be planted in a rectangular field which is 32 m long and 30 m wide if each tree needs 4 m² to grow.

3. Calculate the area of the quadrilateral that results from drawing lines between the midpoints of the sides of a rectangle whose base and height are 8 and 6 cm respectively.

4. Calculate the number of square tiles needed to cover a rectangular surface of 4 m by 3 m if the length of each side of the tiles is 10 cm.

5. A rectangular garden has dimensions of 30 m by 20 m and is divided in to 4 parts by two pathways that run perpendicular from its sides. One pathway has a width of 8 dm and the other, 7 dm. Calculate the total usable area of the garden.

6. Calculate the length of the diagonal of a rectangle with a base of 10 cm and a height of 6 cm.

7. A rectangular field has a length of 170 m and a width of 28 m. Calculate:

1 The area of the field in hectares.

2 The price to re-seed the field if each square meter costs $15.

Trapezium Problems

1. Find the area of the following trapezium:

[pic]

2. A wooded area is in the shape of a a trapezium whose bases measure 128 m and 92 m and its height is 40 m. A 4 m wide walkway is constructed which runs perpendicular from the two bases. Calculate the area of the wooded area after the addition of the walkway.

3. A line connects the midpoint of BC (Point E), with Point D in the square ABCD. Calculate the area of the acquired trapezium shape if the square has a side of 4 m.

4. The perimeter of an isosceles trapezium is 110 m and the bases are 40 and 30 m in length. Calculate the length of the non-parallel sides of the trapezium and its area.

5. If non-parallel sides of an isosceles trapezium are prolonged, an equilateral triangle with sides of 6 cm would be formed. Knowing that the trapezium is half the height of the triangle, calculate the area of the trapezium.

6. Find the height of the following isosceles trapezium:

[pic]

7. Calculate the oblique side of the right trapezium:

[pic]

From several pages on the Internet (, , , om….)

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