Question

The diagram shows some land in the shape of a quadrilateral ABCD. AB = 6 km, AD = 5 km and CD = 12 km Angle BAC = 30 The land is sold for £10 million per square kilometre. Calculate the total cost of the land.

Answer 1

£495 million

Explanation:

To find out the total cost of the land, we need to first calculate the area of the land.

Step 1: Find area of right angled triangle ADC

AD = 5 km,

DC = 12 km

Area of the right triangle = ½*a*b

a = 5km

b = 12km

Area = ½*5*12

= 5*6

Area of ADC = 30 km²

Step 2: Find the area of triangle ABC

First, let's find the length of AC using Pythagorean theorem

AC² = AD² + DC²

AC² = 5² + 12² = 25 + 144

AC = √169

AC = 13km

Area of ∆ABC = ½*AB*AC*sin(30°)

= ½*6*13*0.5

= 3*13*0.5

Area of ∆ABC = 19.5 km²

Total area of the land = area of ∆ADC + ∆ABC = 30 + 19.5 = 49.5 km²

Step 3: calculate how much the land costs

If the land costs £10 million per km²,

Cost of 49.5 km² = 49.5 × 10 = £495 million