Area of Some Polygons

Geometry Area Quiz

Created by: MR/Nasef.N

Area of Triangles

1. What is the area of a right triangle with legs of 6 cm and 8 cm?

A) \(14 \text{ cm}^2\)

B) \(24 \text{ cm}^2\)

C) \(24 \text{ cm}^2\)

D) \(48 \text{ cm}^2\)

2. The formula for the area of an acute triangle is:

A) \(\frac{1}{2} \times \text{base} \times \text{height}\)

B) \(\text{base} \times \text{height}\)

C) \(\frac{1}{2} \times \text{sum of all sides}\)

D) \(\text{side}^2\)

3. An obtuse triangle has sides 5 cm, 6 cm, and 10 cm. If the height corresponding to the 6 cm base is 4 cm, what is its area?

A) \(10 \text{ cm}^2\)

B) \(12 \text{ cm}^2\)

C) \(15 \text{ cm}^2\)

D) \(30 \text{ cm}^2\)

4. If the area of a right triangle is \(30 \text{ cm}^2\) and one leg is 5 cm, what is the length of the other leg?

A) 6 cm

B) 12 cm

C) 10 cm

D) 15 cm

5. Two triangles have the same base and height. What can you say about their areas?

A) They are equal

B) The acute triangle has larger area

C) The right triangle has larger area

D) The obtuse triangle has larger area

Area of Quadrilaterals

6. What is the area of a square with diagonal \(5\sqrt{2}\) cm?

A) \(10 \text{ cm}^2\)

B) \(20 \text{ cm}^2\)

C) \(25 \text{ cm}^2\)

D) \(50 \text{ cm}^2\)

7. A rectangle has length 12 cm and area \(84 \text{ cm}^2\). What is its width?

A) 6 cm

B) 7 cm

C) 8 cm

D) 9 cm

8. The area of a rhombus with diagonals 10 cm and 8 cm is:

A) \(18 \text{ cm}^2\)

B) \(40 \text{ cm}^2\)

C) \(40 \text{ cm}^2\)

D) \(80 \text{ cm}^2\)

9. A trapezoid has parallel sides of 5 cm and 9 cm, and height 4 cm. What is its area?

A) \(14 \text{ cm}^2\)

B) \(20 \text{ cm}^2\)

C) \(28 \text{ cm}^2\)

D) \(36 \text{ cm}^2\)

10. The area of a parallelogram with base 15 cm and height 6 cm is:

A) \(21 \text{ cm}^2\)

B) \(30 \text{ cm}^2\)

C) \(90 \text{ cm}^2\)

D) \(45 \text{ cm}^2\)

11. If the side of a square is increased by 50%, its area increases by:

A) 50%

B) 100%

C) 125%

D) 150%

12. A rectangle and a parallelogram have the same base and height. How do their areas compare?

A) They are equal

B) Rectangle has larger area

C) Parallelogram has larger area

D) It depends on the angles

13. The area of a rhombus is \(24 \text{ cm}^2\) and one diagonal is 6 cm. What is the other diagonal?

A) 4 cm

B) 8 cm

C) 12 cm

D) 18 cm

14. What is the height of a trapezoid with area \(45 \text{ cm}^2\) and parallel sides of 7 cm and 11 cm?

A) 4 cm

B) 5 cm

C) 6 cm

D) 7 cm

15. A parallelogram has area \(56 \text{ cm}^2\) and base 8 cm. What is its height?

A) 6 cm

B) 7 cm

C) 7 cm

D) 8 cm

16. Which shape always has equal diagonals?

A) Rectangle

B) Rhombus

C) Parallelogram

D) Trapezoid

17. The area of a right triangle is half the area of a rectangle with the same:

A) Base and height

B) Perimeter

C) Diagonal

D) Angles

18. If the sides of a square are doubled, the area becomes:

A) Double

B) Triple

C) Four times

D) Half

19. A kite has diagonals of 12 cm and 16 cm. Its area is:

A) \(28 \text{ cm}^2\)

B) \(56 \text{ cm}^2\)

C) \(96 \text{ cm}^2\)

D) \(192 \text{ cm}^2\)

20. Which formula is correct for the area of a trapezoid?

A) \(\text{base} \times \text{height}\)

B) \(\frac{1}{2} \times (\text{base}_1 + \text{base}_2) \times \text{height}\)

C) \(\frac{1}{2} \times \text{diagonal}_1 \times \text{diagonal}_2\)

D) \(\text{side}^2\)

Drawing and Essay Questions

1. Draw a right triangle with legs 3 cm and 4 cm. Calculate its area and mark all measurements on your diagram.

[Space for drawing]

2. Draw a rectangle with length 5 cm and width 3 cm adjacent to a parallelogram with the same base and height. Show that they have equal areas.

[Space for drawing]

3. Construct a rhombus with diagonals 6 cm and 8 cm. Calculate its area using the diagonal formula and verify by dividing it into triangles.

[Space for drawing]

4. Draw an isosceles trapezoid with parallel sides 4 cm and 8 cm, and non-parallel sides 5 cm each. Calculate its area and show your work.

[Space for drawing]

5. Draw an obtuse triangle and show how its area can be calculated by dividing it into two right triangles. Label all necessary measurements.

[Space for drawing]

Created by: MR/Nasef.N