Question

The diagram shows a rectangle PQRS.

Answer 1

Answer:

a) The area of the triangle AQB is 43 square centimeters.

b) The length of the line segment AQ is approximately 14.866 centimeters.

Step-by-step explanation:

a) The procedure consist in subtracting the areas of triangles APQ, ASB and BRQ of the area the rectangle, that is to say:

$A = (9\,cm)\cdot (14\,cm) - \frac{1}{2}\cdot (5\,cm)\cdot (14\,cm) - \frac{1}{2}\cdot (8\,cm)\cdot (9\,cm) -\frac{1}{2}\cdot (4\,cm) \cdot (6\,cm)$

$A = 43\,cm^{2}$

The area of the triangle AQB is 43 square centimeters.

b) The length of the line segment AQ is determined by Pythagorean Theorem:

$AQ = \sqrt{AP^{2}+PQ^{2}}$ (1)

$AQ = \sqrt{(5\,cm)^{2}+(14\,cm)^{2}}$

$AQ \approx 14.866\,cm$

The length of the line segment AQ is approximately 14.866 centimeters.