Trapezium PQRT is formed by joining a square PQRS and a right angled triangle as shown below. PS = ST = 4cm. What is the area of the trapezium PQRT?
Answers
Answer: The area of the trapezium PQRT is 17.5 square centimeters.
Step-by-step explanation:
To find the area of the trapezium PQRT, we first need to find the lengths of its two parallel sides.
From the given figure, we can see that PQRS is a square. Therefore, PQ = QR = RS = PS = 4 cm.
Let us now consider the right-angled triangle PRT. We know that PS = ST = 4 cm, and we also know that angle RPT is a right angle. Therefore, using the Pythagorean theorem, we can find the length of the hypotenuse PT as follows:
PT² = PR² + RT²
PT² = (4 cm)² + (3 cm)²
PT² = 16 cm² + 9 cm²
PT² = 25 cm²
PT = 5 cm
Now, we can see that PQ and RT are parallel sides of the trapezium. The length of PQ is 4 cm, and the length of RT is 3 cm. Therefore, the area of the trapezium is:
Area = (1/2) x (sum of parallel sides) x (distance between parallel sides)
Area = (1/2) x (4 cm + 3 cm) x (PT)
Area = (1/2) x 7 cm x 5 cm
Area = 17.5 cm²
Therefore, the area of the trapezium PQRT is 17.5 square centimeters.
Learn more about Trapezium :
https://brainly.in/question/51526398
#SPJ2