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7.11D Finding the Area of Any Triangle: Fluency and Exam Drill

EDEXCEL Edexcel 1MA1 · Calculator allowed · about 55 minutes

Total Marks

Name: _______________________________ Date: ____ / ____ / ______

Answer ALL questions. Show all your working.

Work out the area of a triangle with two sides 6 cm and 8 cm and included angle 90 degrees.

(Total for Question 1 is 1 mark)

Find the area of a triangle with sides 7 cm and 5 cm and included angle 30 degrees.

(Total for Question 2 is 1 mark)

Find the exact area of a triangle with sides 9 cm and 10 cm and included angle 60 degrees. Give your answer in surd form.

(Total for Question 3 is 2 marks)

The area of triangle ABC is 10 cm². Side AB = 5 cm and side AC = 6 cm. Work out the size of angle A. Give your answer to the nearest degree.

(Total for Question 4 is 3 marks)

Calculate the area of a triangle with sides 12 cm and 7 cm and included angle 120 degrees. Give your answer to 1 decimal place.

(Total for Question 5 is 2 marks)

The area of a triangle is 28 cm². One side is 9 cm and the included angle is 50 degrees. Work out the length of the other side, correct to 2 decimal places.

(Total for Question 6 is 3 marks)

In a triangle, two sides are 8 cm and 13 cm and the area is 26 cm². Find all possible measures of the included angle x, in degrees.

(Total for Question 7 is 3 marks)

A triangular sail has sides 6.5 m and 4.2 m with included angle 37 degrees. Calculate the area of the sail, giving your answer to 2 decimal places.

(Total for Question 8 is 3 marks)

A triangle has area 15 cm². One side is 4 cm and the included angle is 40 degrees. Work out the length of the other side, correct to 2 decimal places.

(Total for Question 9 is 3 marks)

The area of a triangle is 21 cm². Two sides are 7 cm and 9 cm. Work out the included angle to 1 decimal place.

(Total for Question 10 is 3 marks)

Triangle ABC has AB = 14 cm, AC = 10 cm and area 35 cm².
(a) Find all possible values of angle A.
(b) For angle A = 30 degrees, find the length BC, correct to 2 decimal places.

(a)Find all possible values of angle A.(2)

(b)For A = 30 degrees, find BC correct to 2 decimal places.(2)

(Total for Question 11 is 4 marks)

Triangle ABC has AB = 12 m, angle A = 60 degrees and area 84 m². Work out AC, correct to 2 decimal places.

(Total for Question 12 is 5 marks)

Two sides of a triangle are 10 cm and 8 cm and the area is 20 cm².
(a) Find the two possible values of the included angle C.
(b) For each possible angle, find the length of the third side to 2 decimal places.

(Total for Question 13 is 5 marks)

A triangular garden has sides 7.5 m and 11.2 m with included angle 142 degrees.
(a) Calculate the area of the garden to 2 decimal places.
(b) If turf costs £3.50 per square metre, calculate the cost to the nearest penny.

(a)Calculate the area to 2 decimal places.(3)

(b)Calculate the cost of turf at £3.50 per m² to the nearest penny.(2)

(Total for Question 14 is 5 marks)

Triangle ABC has AB = 15 cm, AC = 10 cm and area 36 cm².
Work out angle A and then calculate the length BC. Give the final length BC to the nearest whole number.

(Total for Question 15 is 5 marks)

Mark scheme · 7.11D Finding the Area of Any Triangle: Fluency and Exam Drill

Question 1

B1 24 cm² cao
Answer: 24 cm²

Question 2

B1 8.75 cm² cao
Answer: 8.75 cm²

Question 3

M1 use 1/2 * 9 * 10 * sin60 or equivalent method
A1 45*√3/2 cm² cao
Answer: 45*√3/2 cm²

Question 4

M1 use 1/2 * 5 * 6 * sin A = 10 and form sin A = 2*area/(ab) = 20/30 = 2/3
M1 take arcsin: A = arcsin(2/3) oe
A1 42 degrees cao
Answer: 42 degrees

Question 5

M1 use 1/2 * 12 * 7 * sin120 (sin120 = sin60 = √3/2) oe
A1 36.4 cm² awrt
Answer: 36.4 cm² (awrt)

Question 6

M1 use 1/2 * 9 * b * sin50 = 28 and rearrange to b = 56 / (9 sin50)
M1 substitute and evaluate denominator correctly oe
A1 8.12 cm cao
Answer: 8.12 cm

Question 7

M1 use 1/2 * 8 * 13 * sin x = 26 so sin x = 26/52 = 0.5
M1 know that sin x = 0.5 gives x = 30 degrees or x = 150 degrees oe
A1 30 degrees and 150 degrees cao
Answer: 30 degrees or 150 degrees

Question 8

M1 use 1/2 * 6.5 * 4.2 * sin37 or equivalent substitution
M1 evaluate sin37 and multiply correctly
A1 8.21 m² cao
Answer: 8.21 m²

Question 9

M1 rearrange 1/2 * 4 * b * sin40 = 15 to b = 30 / (4 sin40) or equivalent
M1 substitute value for sin40 and evaluate numerator/denominator correctly
A1 11.67 cm cao
Answer: 11.67 cm

Question 10

M1 use 1/2 * 7 * 9 * sin C = 21 so sin C = 42/63 = 2/3
M1 take inverse sine to find C = arcsin(2/3) oe
A1 41.8 degrees cao
Answer: 41.8 degrees

Question 11

(a) M1 use sin A = 2*area/(AB*AC) = 70/140 = 0.5
(a) A1 30 degrees and 150 degrees cao
(a) Answer: 30 degrees or 150 degrees
(b) M1 use law of cosines: BC² = 14² + 10² - 2*14*10*cos30
(b) A1 7.32 cm cao
(b) Answer: 7.32 cm

Question 12

M1 use 1/2 * AB * AC * sin A = area
M1 substitute: 1/2 * 12 * AC * sin60 = 84
M1 rearrange to AC = 84 / (0.5*12*sin60) or equivalent
M1 evaluate denominator correctly (sin60 = √3/2) and compute AC
A1 16.17 m cao
Answer: 16.17 m

Question 13

M1 use 1/2 * 10 * 8 * sin C = 20 so sin C = 20/40 = 0.5
M1 state C = 30 degrees or 150 degrees
M1 use law of cosines for first case: c² = 10² + 8² - 2*10*8*cos30
M1 calculate first c = 5.04 cm (awrt) and for second case set up c² = 10² + 8² - 2*10*8*cos150
A1 second c = 17.39 cm cao
Answer: C = 30 degrees or 150 degrees; third side lengths approx 5.04 cm and 17.39 cm

Question 14

(a) M1 use 1/2 * 7.5 * 11.2 * sin142
(a) M1 evaluate sin142 correctly (sin142 = sin38) and multiply
(a) A1 25.86 m² awrt
(a) Answer: 25.86 m²
(b) M1 multiply the exact area (25.8578 m²) by 3.50
(b) A1 £90.50 cao
(b) Answer: £90.50

Question 15

M1 use 1/2 * 15 * 10 * sin A = 36 so sin A = 72/150 = 0.48
M1 take inverse sine to find A = arcsin(0.48) oe
M1 use law of cosines: BC² = 15² + 10² - 2*15*10*cos A
M1 substitute cos A and evaluate BC
A1 8 cm cao
Answer: 8 cm

Finding the Area of Any Triangle: Fluency and Exam Drill - Worksheets, Questions and Revision