Quadrangle PQRSA was made by extending each side of quadrangle ABCD as follows.
① The length of the side AP is 3 times of the length of the side AB.
② The length of the side BQ is twice of the length of the side BC.
③ The length of the side CR is 3 times of the length of side CD.
④ The length of the side DS is twice of the length of the side DA.
Answer the following questions.
(1) Find the area ratio of the area of triangle APS and the area of the triangle ABD.
(2) Find the area ratio of the area of quadrangle PQRS and the area of quadrangle ABCD.
(3) When the multiplying factor is 50 times of ① and ③, and 100 times of ② and ④, find the area ratio of the area of quadrangle PQRS and the area of quadrangle ABCD.
① The length of the side AP is 3 times of the length of the side AB.
② The length of the side BQ is twice of the length of the side BC.
③ The length of the side CR is 3 times of the length of side CD.
④ The length of the side DS is twice of the length of the side DA.
Answer the following questions.
(1) Find the area ratio of the area of triangle APS and the area of the triangle ABD.
(2) Find the area ratio of the area of quadrangle PQRS and the area of quadrangle ABCD.
(3) When the multiplying factor is 50 times of ① and ③, and 100 times of ② and ④, find the area ratio of the area of quadrangle PQRS and the area of quadrangle ABCD.
Answer
(1) 3 : 1
(2) 8 : 1
(3) 9851 : 1
(2) 8 : 1
(3) 9851 : 1
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