Question

The diagram represents the cross-sections of a loft PQRST, PTQ is an isosceles triangle and QRST is
a rectangle.
The height PN of P above the ground is 75 m.The height QR is 5 m and PQ is 6.5 m. Given that N is the mid-point of SR, find the length
of SR and the area of PQRST.
​

Answer 1

Answer:

SR = 12 m, Area of PQRST = 75 m²

Step-by-step explanation:

Here, PQ = 6.5 m, PN = 7.5 m , QR = 5m

Again , MN =QR = 5m

So, PM = PN -MN = (7.5 - 5) m = 2.5m

Now , QM = $\sqrt{PQ^2 - PM^2}$ = $\sqrt{6.5^2 - 2.5^2}$ m = 6 m

SR = 2 ×  NR = 2 × QM = (2×6) m = 12 m

Area of PQRST = 2 × area of PQRNM  (It is a trapizium)

                         = 2 × 0.5 × (sum of two parallel sides)× height

                         = 2 × 0.5 × (PN + QR)× QM

                         = 2 × 0.5 × (7.5+5)× 6

                          = 75 m²