Coordinates and trigonometry · Ages 12–13

Areas on the coordinate plane worksheet

Part of: First steps in coordinates

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Coordinates and trigonometry · Ages 12–13

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Write each answer in the space. For word problems, show your working and write a sentence answer.

1.Triangle ABC has corners A(−6, 2), B(6, 2) and C(−1, 0). Its area is square units.
Answer:
2.Triangle ABC has corners A(−3, 1), B(5, 1) and C(−3, −1). Base AB = , height = , area = square units.
Fill in each blank
Answer:
3.Rectangle ABCD has corners A(−3, −3), B(3, −3), C(3, 2) and D(−3, 2). Its area is square units.
Answer:
4.Triangle ABC has corners A(−1, −2), B(1, −2) and C(3, 5). Base AB = , height = , area = square units.
Fill in each blank
Answer:
5.Triangle ABC has corners A(−1, 0), B(2, 0) and C(−2, −6). Its area is square units.
Answer:
6.Triangle ABC has corners A(0, −4), B(0, 3) and C(4, 0). Its area is square units.
Answer:
7.Trapezium ABCD has corners A(−5, −3), B(5, −3), C(2, 1) and D(−2, 1). Its area is square units.
Answer:
8.Triangle ABC has corners A(−4, −2), B(−4, 6) and C(2, 2). Its area is square units.
Answer:
9.Trapezium ABCD has corners A(−2, −5), B(4, −5), C(5, 4) and D(−5, 4). Its area is square units.
Answer:
10.With a rectangle round triangle ABC: the rectangle's area = , the three corner right triangles together , so triangle ABC = square units.
Fill in each blank
Answer:
11.The area of quadrilateral ABCD is square units.
Answer:

13.Triangle ABC has area 12 square units, with A(−3, 0) and B(3, 0), and C above AB on the y-axis. What is C's y-coordinate?
Working:
Answer:
14.A kite's frame is drawn on a coordinate plane with corners A(−2, 0), C(0, 2), B(4, 0) and D(0, −6). What is the area of kite ACBD, in square units?
Working:
Answer:
15.On a map, a triangular lawn has corners A(−1, 0), B(6, 0) and C(−1, 5). Which working gives its area?
- A. 12 × (6 − 1) × 5
- B. 12 × (6 + 1) × 1
- C. 12 × (6 + 1) × 5
- D. (6 + 1) × 5
Choose the right answer
Working:
Answer:
16.O is the origin, A(−1, 0), and P on the y-axis above the x-axis. Triangle OAP has area 4 square units. What is P's y-coordinate?
Working:
Answer:
17.A rectangular garden has corners (−4, −2), (4, −2), (4, 4) and (−4, 4), with a square pond at (0, 0), (1, 0), (1, 1) and (0, 1). Garden = , pond = , area left for flowers = square units.
Fill in each blank
Working:
Answer:
18.A house's end wall is a pentagon with corners (−4, 0), (4, 0), (4, 6), (0, 7) and (−4, 6). Split into a rectangle and a triangle: rectangle = , triangle = , pentagon = square units.
Fill in each blank
Working:
Answer:

Show the answers and working

Areas on the coordinate plane worksheet: Answers and working

1. 12
AB is horizontal: base = 6 + 6 = 12; the height is C's distance up or down to AB, 2; area = 12 × 12 × 2 = 12.
2. 8, 2, 8
AB is horizontal, so the base is the gap in x, 8; the height is the gap in y from C to AB, 2; 12 × 8 × 2 = 8.
3. 30
Length AB = 3 − (−3) = 6, width BC = 2 − (−3) = 5, area = 6 × 5 = 30.
4. 2, 7, 7
AB is horizontal, so the base is the gap in x, 2; the height is the gap in y from C to AB, 7; 12 × 2 × 7 = 7.
5. 9
AB is horizontal: base = 2 + 1 = 3; the height is C's distance up or down to AB, 6; area = 12 × 3 × 6 = 9.
6. 14
AB is vertical, so take it as the base: AB = 7; the height is C's distance across to AB, 4; area = 12 × 7 × 4 = 14.
7. 28
AB and DC are both horizontal, the parallel sides: AB = 10, DC = 4, height 4; area = 12 × (10 + 4) × 4 = 28.
8. 24
AB is vertical, so take it as the base: AB = 8; the height is C's distance across to AB, 6; area = 12 × 8 × 6 = 24.
9. 72
AB and DC are both horizontal, the parallel sides: AB = 6, DC = 10, height 9; area = 12 × (6 + 10) × 9 = 72.
10. 40, 26, 14
The rectangle round it: 5 × 8 = 40; the three corners 15 + 3 + 8 = 26; 40 − 26 = 14.
11. 21
AC lies on the x-axis and cuts it into triangles ABC and ACD: AC = 7, so the area is 12 × 7 × 1 + 12 × 7 × 5 = 3.5 + 17.5 = 21.

12. C. 21
AB is horizontal: base = 2 − (−5) = 7, height = C's distance to AB, 6, area = 12 × 7 × 6 = 21.

Marking: 2 for the working, 1 for the answer, 1 for the sentence.

13. 4
Base AB = 3 + 3 = 6; 12 × 6 × height = 12, so the height is 4. C is 4 above AB: 0 + 4 = 4.
14. 24
AB on the x-axis splits it into triangles ABC and ABD: AB = 6, and their heights add to 2 + 6 = 8, so the area is 12 × 6 × 8 = 24.
15. C. 12 × (6 + 1) × 5
AB lies on the x-axis, 6 + 1 long; the height is C's y, 5. Area = 12 × (6 + 1) × 5.
16. 8
OA = 1 is the base and OP the height: 12 × 1 × OP = 4, so OP = 8 and P is (0, 8).
17. 48, 1, 47
Garden (4 + 4) × (2 + 4) = 48; pond 1 × 1 = 1; the difference is 47.
18. 48, 4, 52
Rectangle 8 × 6 = 48; the roof triangle has base 8 and height 7 − 6 = 1: 12 × 8 × 1 = 4; together 52.

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