![](data:image/svg+xml;utf8,<svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" viewBox="0 0 72 71" width="72"></svg>)
The figure below is a square made of a jigsaw puzzle. It is known that the square has an area of 64 square centimeters. Find the sum of the areas of Figure 1 and Figure 2
Figure 2: 64.1 / 4 = 16 (CM) Figure 1: 16.1 / 2 = 8 (CM)
As shown in the figure, it is known that the side length of square ABCD is 10 cm, point E is on side AB, and AE = 4 cm. If point P moves from point B to point C at a speed of 2 cm / s on line BC, and point Q moves from point C to point D on line CD, let the motion time be T seconds. (1) if the motion speed of point q is equal to that of point P, after 2 seconds, are △ BPE and △ CQP identical? Please explain the reason; (2) if the velocity of point q is not equal to that of point P, then when t is the value, it can make △ BPE and △ CQP congruent; at this time, what is the velocity of point q
(1) The results show that △ BPE and △ CQP are congruent. (1 min) ∵ the velocity of point q is equal to that of point P, and T = 2 seconds ∵ BP = CQ = 2 × 2 = 4cm (2 min) ∵ AB = BC = 10cm, AE = 4cm, ∵ be = CP = 6cm, ∵ quadrilateral ABCD is square, ∵ in RT ∵ BPE and RT ∵ CQP, BP = cqbe = CP,
RELATED INFORMATIONS
- 1. In the square ABCD with a side length of 96 cm (as shown in the figure), e, F and G are the quartering points on BC, and m, N and P are the quartering points on AC. what is the area of the shadow?
- 2. How many circles with a diameter of 30 cm can be cut out on the 180 cm long and 120 cm wide cardboard? GO GOGO Give the answer in ten minutes!
- 3. There is a biggest square in the circle. The side length of the square is 5 decimeters. What is the area of the circle
- 4. Using a piece of square paper with a side length of 2 decimeters, cut a circle as large as possible. The area of the circle is () A. 3.14 square decimeters B. 12.56 square decimeters C. 6.28 square decimeters D. 24.92 square decimeters
- 5. Cut a rectangular paperboard 12 cm long and 8 cm wide into the largest semicircle. What is the area of the remaining paperboard after cutting it?
- 6. In a 12 decimeter long, 10 decimeter wide rectangular cardboard cut a largest circle, the remaining cardboard is how many square decimeters?
- 7. With 12 cm long, 10 cm wide rectangular cardboard put together into a square, at least how many pieces of cardboard?
- 8. A rectangular cardboard is 10 decimeters long and 7 decimeters wide. How many circles can you cut from the paper with a radius of 1.5 decimeters?
- 9. A factory uses rectangular and square cardboard as shown in figure a to make vertical and horizontal rectangular cartons as shown in Figure B
- 10. A factory uses the rectangular and square cardboard as shown in figure a to make the vertical and horizontal rectangular paperboards as shown in Figure B. (the width of the rectangle is equal to the side length of the square) (1) At present, there are 50 square cardboard and 100 rectangular cardboard ① According to the meaning of the question, complete the following table: Vertical carton (piece) horizontal carton (piece) x y Square cardboard x () Rectangular paperboard (sheet) () 3Y (2) If all the cardboard is used up, find the value of X and y (3) If there are 80 pieces of square cardboard and N pieces of rectangular cardboard to make the above two kinds of cartons, the cardboard is just used up, and 162 < n < 172 is known, the value of n is calculated Do it once with binary
- 11. 1. It is known that the length of the hypotenuse of an isosceles right triangle is 10cm, and the waist length of the isosceles triangle is calculated 2. There are four identical right triangles to form a large square. As shown in the figure, it is known that the lengths of the two right sides of a right triangle are 6cm and 8cm respectively. To find the area of a large square, the Pythagorean theorem is used in both problems
- 12. As shown in the figure, in the square ABCD, e is the midpoint of AB side, G and F are the points on AD and BC side respectively. If Ag = 1, BF = 2, ∠ GEF = 90 °, then the length of GF is______ ．
- 13. As shown in Figure 1, slide the right angle vertex P of a right angle triangle plate on the diagonal BD of square ABCD, and make one right angle edge pass through point a all the time, and the other right angle edge intersects with BC at point E (1) Verification: PA = PE; (2) if the square in (1) is changed into a rectangle, and other conditions remain unchanged (as shown in Figure 2), and ad = 10, DC = 8, calculate AP: PE; (3) under the condition of (2), when p slides to the extension line of BD (as shown in Figure 3), please write the ratio of AP: PE directly
- 14. As shown in the figure, place the right angle vertex P of the triangle plate PMN on the diagonal BD of the square ABCD, and rotate the triangle plate around point P. the two right angle sides PM and PN of the triangle plate intersect AB at e and BC at f respectively (1) Verification: PE = PF (2) The quantitative relationship among be, BF and BP is expressed by equation and explained
- 15. Cut a square on the sheet iron of a right triangle (bottom 40, height 10). The area of the square is as large as possible. How about the area of the square?
- 16. Cut the largest square from the sheet iron of a right triangle. What's the area of the square? (40 meters at the bottom) 40 / 10 = 4 40 * 10 / 2 / (1 + 4) = 40 (M2) 40 * 2 / 10 = 8 (m) 8 * 8 = 64 (m)
- 17. The two right sides of a right triangle are 30cm and 40cm long, and the hypotenuse is 50cm long. The area of this triangle is______ Square centimeter
- 18. The right side of a right triangle is divided into 40 cm and 10 cm. Cut out a square and make it as large as possible. What is the square area Sorry, wrong number. Change the word "person" to "person", Can you solve it arithmetically?
- 19. Cut a piece of square paper with a side length of 36 cm into four identical small rectangular pieces. The sum of the circumference of the four small rectangular pieces is larger than that of the original square How many centimeters has the circumference increased?
- 20. Cut the square cardboard with side length of 20cm into four small squares of the same size. How many centimeters is the circumference of each small square