Area of a triangle Questions and Answers

Area of a triangle Questions

1. The sides of a triangle are in the ratio 3:5:6. If its perimeter is 56 cm, use the Heroes formula to find its area (4mks)

2. The figure below is a triangle XYZ. ZY = 13.4cm, XY = 5cm and angle xyz = 57.7^o

Calculate

1. Length XZ. (3mks)
2. Angle XZY. (2 mks)
3. If a perpendicular is dropped from point X to cut ZY at M, Find the ratio MY:ZM. (3 mks)
4. Find the area of triangle XYZ. (2 mks)

3. The figure below represents a triangular plot ABC. The lengths of AB = 50m, AC = 80m

 and angle BAC =30^o

(a) Find the length of BC to 2 s.f

(b) Find the area of the plot in hectares

(c) The plot is fenced using 4 strands of barbed wire. The length of one roll of barbed

wire is 600m and it costs shs.4000. Calculate;

 (i) The length of fencing wire required

 (ii) The number of complete rolls to be bought

 (iii) The cost of the rolls

Area of a triangle Answers

1. a) BC² = 50² + 80² – 2 x 50 x 80 cos30

= 2500 + 6400 – 6928.20 = 1971.8

 BC =√ 1971.8

= 44.40m

= 44m

b) Area of the plot

= ½ x 50 x 80 x sin30 = 1000m²

= (1000) ha

10000

= 0.01ha

c) i) Length of wire required

= (50 + 80 + 44) x 4 = 696m

ii) Complete rolls to be bought = 2

iii) Cost ( 2 x 4000) = Shs.8000