Question

The sides of a quadrilateral, taken in order are 5, 12, 14 and 15 meters respectively, and the angle contained by the first two sides is a right angle. Find its are

 

Answer 1

Given that sides of quadrilateral are AB = 5 m, BC = 12 m, CD = 14 m and DA = 15 m
AB = 5m, BC = 12m, CD = 14 m and DA = 15 m
Join AC

Area of ΔABC = `1/2`×𝐴𝐵×𝐵𝐶       [∵𝐴𝑟𝑒𝑎 𝑜𝑓 Δ𝑙𝑒=`1/2`(3𝑥+1)]

= `1/2×5×12`

= 30 cm2

In ΔABC By applying Pythagoras theorem.

`AC^2=AB^2+BC^2`

`⇒AC=sqrt(5^2+12^2)`

`⇒sqrt(25+144)`

`⇒sqrt169=13m`

𝑁𝑜𝑤 𝑖𝑛 Δ𝐴𝐷𝐶
Let 2s be the perimeter

∴ 2s = (AD + DC + AC)

⇒ S = `1/2`(15+14+13)=`1/2`×42=21𝑚

By using Heron’s formula

∴ Area of ΔADC = `sqrt(S(S-AD)(S-DC)(S-AC))`

`=sqrt(21(21-15)(21-14)(21-13))`

`sqrt(21xx6xx7xx8)`

∴𝐴𝑟𝑒𝑎 𝑜𝑓 𝑞𝑢𝑎𝑑𝑟𝑖𝑙𝑎𝑡𝑒𝑟𝑎𝑙 𝐴𝐵𝐶𝐷=𝑎𝑟𝑒𝑎 𝑜𝑓 (Δ𝐴𝐵𝐶)+𝐴𝑟𝑒𝑎 𝑜𝑓 (Δ𝐴𝐷𝐶) = 30 + 84 = `114 m^2`