Question

find the area of a quadrilateral PQRS in which angle QPS =angle SQR=90 ,PQ=12 CM, PS=9CM, QR=8CM AND SR=17 CM

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Answer 1

Answer:

the area of a quadrilateral PQRS in which angle QPS =angle SQR=90 ,PQ=12 CM, PS=9CM, QR=8CM AND SR=17 CM is 114 cm²

Step-by-step explanation:

Given that Angle QPS = angle SGR = 90°, we have two right angled triangles.

They are: Triangle PQS and triangle QRS.

For triangle QRS we need to get one of the shorter sides since we only have the hypotenuse and one shorter side.

The sides of QRS are: SR = 17 cm and QR = 8 cm

We need QS. Using Pythagorean theorem we have:

QS = √(17² - 8²) = 15 cm

Area of QRS = 1/2 × 15 × 8 = 60 cm²

Area of QPS we have:

PQ = 12 cm  PS = 9 cm

Area = 1/2 × 12 × 9 = 54 cm²

The area of the quadrilateral is equal to the sum of the area of the two triangles.

So, we have:

Area = 60 + 54 = 114 cm²