Look at the measures shown in the adjacent figure and find the area of ☐ PQRS.
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Look at the measures shown in the adjacent figure and find the area of ☐ PQRS.
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Verified answer
Given:
✰ PS = 36 m
✰ SR = 15 m
✰ RQ = 25 m
✰ PQ = 56 m
To find:
✠ The area of ☐ PQRS.
Solution:
❖ Let's understand the concept first! First of all we will find the area of ∆PSR and then the are of ∆PQR. To find the area of ∆PSR, we will simply use formula of triangle, but to find the area of ∆PQR, first we will calculate it's side PR, then using Heron's formula we will calculate it's area. After that we will add both the area of ∆PSR and the area of ∆PQR to get the area of whole figure i.e, of ☐ PQRS.
✭Area of triangle = 1/2 × base × height✭
Now,
By using Pythagoras theorem,
⇾H² = B² + P²
⇾PR² = SR² + PS²
⇾PR² = 15² + 36²
⇾PR² = 225 + 1296
⇾PR² = 1521
⇾PR = √1521
⇾PR = 39
Using Heron's formula,
✭ Semi-perimeter ( S ) = (a+b+c)/2 ✭
✭ Area of triangle = √s( s - a ) ( s - b ) ( s - c ) ✭
➤ Area of ☐ PQRS = Area of ∆PSR + Area of ∆PQR
➤ Area of ☐ PQRS = ( 270 + 420 ) m²
➤ Area of ☐ PQRS = 690 m²
∴ The area of ☐ PQRS = 690 m²
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