Question

What is the area of quadrilateral QRST if QS=18 and RT=24. Show work.

Answer 1

`\text{Area of quadrilateral QRST}=216`

Explanation:

Please find the attached image for the quadrilateral QRST.

We have been given that
`QS=18 \text{ and } RT=24`. We are asked to find the area of quadrilateral QRST.

Upon looking at the image of quadrilateral QRST, we can see that quadrilateral QRST is a kite as it has one pair of diagonally opposite equal angles (98 degrees).

We know that area of kite is equal to half the product of its diagonal.

We can see from our image that QS and RT are diagonal of kite, so the area of quadrilateral QRST would be:

`\text{Area of quadrilateral QRST}=(QS\cdot RT)/(2)`

`\text{Area of quadrilateral QRST}=(18\cdot 24)/(2)`

`\text{Area of quadrilateral QRST}=(432)/(2)`

`\text{Area of quadrilateral QRST}=216`

Therefore, the area of quadrilateral QRST is 216 square units.