Question

. Kite QRST has a short diagonal of QS and a long diagonal of RT. The diagonals intersect at point P. Side QR = 17m, diagonal QS = 30m, and segment PT = 25m. Find the area of kite QRST.
8m2
33m2
495m2
990m2

Answer 1

Answer:

495 meter²

Step-by-step explanation:

In the given kite QRST,

PQ = PS = 15 meter

QR = 17 meter

We have to find the area of the kite.

Since kite is in the form of a rhombus.

and rhombus is = $\frac{1}{2}$  (Diagonal QS) × (Diagonal RT)

In Δ QRP,

17² = 15² + RP²

$\sqrt{17^{2}-15^{2}} = RP$

$RP=\sqrt{289-225}$

= √64 = 8 meters.

So RT = RP + PT = 8 + 25 = 33 meter.

Now area of kite = $\frac{1}{2}$ (30) (33) = 495 meter²