Perimeter & Area of Plane Figures
Shinglee Think Mathematics 1B — Chapter 12
Prepared by Miss Clarissa Ng
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www.clartutors.com
Q1. Convert the following areas into cm²:
(a) 3 m²
(b) 4.7 m²
(c) 6.8 m²
(d) 9.2 m²
Q2. The area of the triangle below is 18 cm². Find the height, h, of the triangle.
Q3. The area of the rectangle below is 24 cm². Find
(a) the breadth, b, of the rectangle,
(b) the perimeter of the rectangle.
Q4. The figure below shows a triangle removed from a square. Find the area of the shaded region.
Q5. Find the perimeter and area of each shaded region. (Take π = 3.14)
(a)
(b)
(c)
(d)
Q6. The figure below shows four quadrants removed from a rectangle. Find the area of the shaded region. (Take π = 3.14)
Q7. The figure below shows a right-angled triangle ABC. Find the area of the shaded region. (Take π = 3.14)
Q8. The figure below shows a triangle ABC where AB = 10 cm, BC = 8 cm and AC = 6 cm. If the area of △ABC is 24 cm², find the length of the altitude AD.
Q9. The figure below shows a rectangular field ABCD with a concrete path along the sides AB and BC. Find the area of the concrete path.
Q10. The figure below shows a rectangle ABCD with E on BC and F on AD. If AB = 8 cm, BC = 12 cm, BE = 4 cm and DF = 3 cm, find the area of the shaded region AECF.
Q11. (OPEN) Two rectangles have the same area but different perimeters. Give an example of two such rectangles and calculate their areas and perimeters.
Q12. The figure below shows two intersecting circles with centres O and P. The radius of each circle is 7 cm. If OP = 7 cm, find the area of the shaded region. (Take π = 3.14)
Q13. A goat is tethered by a rope of length 7 m to a post at the corner of a rectangular barn. Find the area of grass the goat can eat in 2 hours if it takes 15 minutes to eat the grass in an area of 10 m². (Take π = 3.14)
Q1. The figure below shows a parallelogram ABCD. Find
(a) the perimeter of the parallelogram,
(b) the area of the parallelogram.
Q2. The figure below shows a rhombus PQRS. Find
(a) the perimeter of the rhombus,
(b) the area of the rhombus.
Q3. Complete the table for each parallelogram:
| Base (cm) | Height (cm) | Area (cm²) |
|---|---|---|
| 8 | 5 | |
| 12 | 48 | |
| 7 | 56 |
Q4. The figure below shows a parallelogram ABCD. If the area of the parallelogram is 60 cm², find the length of BC.
Q5. The area of a rhombus is 120 cm². If the height of the rhombus is 8 cm, find its perimeter.
Q6. The figure below shows a circle with centre O inscribed in a rectangle ABCD. Find the area of the shaded region. (Take π = 3.14)
Q7. The figure below shows a trapezium PQRS. Find
(a) the perimeter of the trapezium,
(b) the area of the trapezium.
Q8. Complete the table for each trapezium:
| Sum of parallel sides (cm) | Height (cm) | Area (cm²) |
|---|---|---|
| 20 | 8 | |
| 30 | 90 | |
| 6 | 72 |
Q9. The figure shows a trapezium PQRS where PQ = 12 m and PS = 13 m. If PT = 10 m, and the area and the perimeter of the trapezium are 185 m² and 61 m respectively, find the length of
(i) RS,
(ii) QR.
Q10. In the figure, ABFG and CDEF are two parallelograms such that the sum of their areas is 702 cm². If AB = CD = EF = FG = ½ BC, find the area of the shaded region.
Q11. Nadia wants to stick duct tape on her suitcase to form the letter 'N' for easy identification. The diagram shows her design for the letter 'N', where AE = 22 cm, AK = 18 cm and AB = CD = DE = FG = HI = IJ = 5 cm. Calculate the total area of the duct tape she needs to form the letter.
Q12. Find the area of the shaded region, where O is the centre of the circle. (Take π = 3.14)
Q13. The cross section of a foot stool and its dimensions are shown in Fig. (a):
(i) Find the area of the cross section of the stool.
(ii) The manufacturer is considering changing the cross section of this stool to that shown in Fig. (b), where arc ABC is a semicircle.
Calculate the percentage increase or decrease in the area of the cross section.
Q14. Raju cut out the various shapes (shown in Fig. (a)) from an A4-sized coloured paper to make a 2D representation of the Eiffel Tower (shown in Fig. (b)) when pieced together. AB, CD, EF, GH, IJ, KL and NP are parallel to one another. Arc LMN is a semicircle. If an A4-sized paper has dimensions 210 mm by 297 mm, find the percentage of paper he used to make this representation.
Q15. In the figure, ABCD is a parallelogram, and AFE and BCE are straight lines. If the area of the parallelogram is 80 cm², BC = CE and DF = FC, find the area of
(i) △ABE,
(ii) △ADF.
Q16. In the figure, ABCD is a parallelogram and AED is a right-angled triangle. If the area of △AED is 25 cm², and the lengths of AE and EB are in the ratio 1 : 3, find the area of the trapezium BCDE.
Q17. (OPEN) On a sheet of graph paper, draw
(a) two parallelograms of different dimensions but with the same area of 10 cm²,
(b) two trapeziums of different dimensions but with the same area of 10 cm².
| Q1(a) | 40,000 cm² |
| Q1(b) | 650,000 cm² |
| Q1(c) | 28,000 cm² |
| Q1(d) | 37,500 cm² |
| Q2 | 6.4 cm |
| Q3(a) | Breadth: 8 cm |
| Q3(b) | Perimeter: 30 cm |
| Q4 | 126 cm² |
| Q5(a) | P = 38.8 cm, A = 72.24 cm² |
| Q5(b) | P = 39.7 cm, A = 10.75 cm² |
| Q5(c) | P = 20.56 cm, A = 25.12 cm² |
| Q5(d) | P = 30.84 cm, A = 37.68 cm² |
| Q6 | 73.76 cm² |
| Q7 | 12.87 cm² |
| Q8 | 4.8 cm |
| Q9 | 64 m² |
| Q10 | 32 cm² |
| Q11 | e.g. 2×12 (A=24, P=28) and 3×8 (A=24, P=22) |
| Q12 | 57.96 cm² |
| Q13 | 153.86 m² |
| Q1(a) | Perimeter: 32 cm |
| Q1(b) | Area: 60 cm² |
| Q2(a) | Perimeter: 48 cm |
| Q2(b) | Area: 96 cm² |
| Q3 | (a) 40 cm², (b) h = 4 cm, (c) b = 8 cm |
| Q4 | BC = 12 cm |
| Q5 | Perimeter: 60 cm |
| Q6 | 74.88 cm² |
| Q7(a) | Perimeter: 42 cm |
| Q7(b) | Area: 100 cm² |
| Q8 | (a) 80 cm², (b) h = 6 cm, (c) 24 cm |
| Q9(i) | RS = 25 m |
| Q9(ii) | QR = 13 m |
| Q10 | 189 cm² |
| Q11 | 275 cm² |
| Q12 | 46.32 cm² |
| Q13(i) | 1,087.5 cm² |
| Q13(ii) | Increase of 9.3% |
| Q14 | 62.4% |
| Q15(i) | 80 cm² |
| Q15(ii) | 40 cm² |
| Q16 | 75 cm² |
| Q17 | (OPEN — any valid dimensions with area = 10 cm²) |