1. Calculate the perimeter and area of the figure below. (Unit: cm)
Test center: the perimeter of the rectangle; The circumference of a square; The area of a rectangle or square.
Special topic: understanding and calculation of plane graphics.
Analysis: (1) According to the rectangle perimeter = (length+width)? 2. Area = length? Wide calculation is enough;
(2) According to the square perimeter = side length? 4. Area = side length? Only the side length is calculated.
Solution: solution: (1)C=(2.2+4.8)? 2= 14 (cm);
S=2.2？ 4.8= 10.56 (square centimeter)
Answer: The perimeter of a rectangle is 14 cm and the area is10.56cm 2.
(2)C=2.5？ 4= 10 (cm);
S=2.5？ 2.5=6.25 (square centimeter).
A: The circumference of a square is 10 cm, and the area is 6.25 cm 2.
Comments: This question mainly examines the perimeter and area calculation of rectangles and squares, which can be calculated according to formulas.
2. Calculate the perimeter and area (unit: cm) below.
Test center: perimeter of circle and ring; The area of a circle or ring.
Special topic: understanding and calculation of plane graphics.
Analysis: According to the circumference of the circle =? d=2？ R, the area of the circle =? R2, replace the answer with data.
Solution: Solution: (1) Perimeter: 3. 14? 6= 18.84 (cm)
Area: 3. 14? (6? 2)2
=3. 14? nine
=28.26 square centimeters
(2) The circumference is: 2? 3. 14? 3.5=2 1.98 (cm)
Area: 3. 14? 3.52
=3. 14? 12.25
=38.465 (square centimeter)
Comments: This question examines the calculation and application of the formula of circumference length and area, which can be solved by memorizing the formula.
3. Find the area below (unit: cm)
Analysis: the area of parallelogram is S=ah, and it can be solved by substituting data.
Answer: Solution: (1)6? 4 = 24(cm2)；
The area of this parallelogram is 24 square centimeters.
(2) 12? 23.5 = 282(cm2)；
The area of this parallelogram is 282 square centimeters.
Comments: This question mainly examines the calculation method of parallelogram area.
4. Look at the picture and calculate the area. (Unit: cm)
Analysis: (1) area of triangle = bottom? Tall? 2. Base 12 cm, height15cm;
(2) Angle area = bottom? Tall? 2. The bottom is 24 cm and the height is 9 cm.
Solution: Solution: (1) 12? 15? 2
= 180? 2
= 90(cm2)；
The area is 90 square centimeters.
(2)24? 9? 2
=2 16? 2
= 108(cm2)；
The area is 108 square centimeter.
Comments: This question mainly examines students' mastery of the triangle area formula.
5. Look at the picture and calculate the area. (Unit: cm)
Analysis: According to the area of trapezoid = (upper bottom+lower bottom)? Tall? 2. Substitute the data to answer.
Solution: Solution: (1)(6.2+ 10.4)? 7.5? 2
= 16.6? 7.5? 2
= 62.25(cm2)；
(2)(4+7)? 6? 2
= 1 1? three
= 33(cm2)；
(3)(30+ 16)? 20? 2
=46? 10
=460(cm2)。
Comments: This topic mainly examines the calculation and application of trapezoidal area formula.
6. Calculate the area below.
Analysis: the area of parallelogram is S=ah, and the area of triangle is S=
1
2
Ah, the area of trapezoid S=(a+b)? h？ 2. Accordingly, it can be solved by substituting data.
Solution: Solution: (1) 10? 4 = 40(cm2)；
The area of this parallelogram is 40 square centimeters.
(2)8? 5? 2 = 20(cm2)；
The area of this triangle is 20 square centimeters.
(3)(24+ 12)? 4? 2 = 72(cm2)；
The area of this trapezoid is 72 square centimeters.
Comments: This topic mainly examines the flexible application of calculation methods of parallelogram, triangle and trapezoid.
7. Find the value of the unknown x in the graph.
Analysis: (1) Area of triangle = length? Wide? 2. According to this, the equations can be listed and solved;
(2) The circumference of a rectangle = (length+width)? 2. According to this, the equations can be listed and solved;
(3)C=2？ R, according to which equations can be listed and solved.
Solution: Solution: (1) Let the side length of the triangle be x cm.
8x？ 2=48
4x=48
x=48？ four
x = 12；
A: The side length of a triangle is 12 cm.
(2) Let the width of the rectangle be x decimeters.
( 16+x)？ 2=52
16+x=52？ 2
x=26- 16
x = 10；
A: The width of a rectangle is 10 decimeter.
(3) Let the radius of the circle be x meters.
2? 3. 14? x= 12.56
6.28x= 12.56
x= 12.56？ 6.28
x = 2；
A: The radius is 2 meters.
Comments: This question mainly examines students' mastery of the formulas of triangle area, rectangle perimeter and circle perimeter.
8. Calculate the area (unit: meter) of the following combined figures.
Analysis: (1) Subtract the area of the triangle from the area of the trapezoid, which is the area of the remaining graph;
(2) The sum of the areas of two rectangles is the area of the combined graph; Answer accordingly.
Solution: Solution: (1)( 15+8.5)? 13? 2-8.5? 4? 2
=23.5? 13? 2-8.5? 4? 2
= 152.75- 17
= 135.75 (m2).
A: The combined map area is 135.75 square meters.
(2)(30- 12)? 20+45? 12
= 18? 20+540
=360+540
=900 square meters.
A: The combined pattern covers an area of 900 square meters.
Comments: this kind of combined graphics: carefully analyze the graphics, cut and fill according to the characteristics of the graphics, and seek the breakthrough point of the problem. Knowledge point: trapezoidal area = (upper bottom+lower bottom)? Tall? 2. Area of triangle = bottom? Tall? 2. Area of rectangle = length? Wide.
9. Calculate the area of the following parts (unit: cm)
Analysis: (1) By observing the graph, we can know that the area of this part is equal to the sum of the area of the triangle above and the area of the square with a side length of 2 cm below, which can be solved by using the area formula.
(2) Observing the figure, we can see that the area of this part is equal to the difference between the area of a rectangle with a length of 20 cm and a width of 16 cm and the area of a trapezoid with a bottom of 3 cm, a bottom of 9 cm and a height of 5 cm on the right, so we can use the area formula to solve it.
Answer: Solution: (1)2? 2+(2+0.3+0.5)? 1.8? 2
=4+2.8? 0.9
=4+2.52
=6.52 (square centimeter);
A: The area of this part is 6.52 square centimeters.
(2)20? 16-(3+9)? 5? 2
=320-30
=290 (square centimeter);
The area of this part is 290 square centimeters.
Comments: This question examines the calculation method of the area of combined graphics, which is generally converted into regular graphics and can be solved by using the area formula.
10. Find the perimeter and area of the picture below. (Unit: cm)
Analysis: (1) According to the graph, the graph consists of a semi-arc length 100, a line segment 100 cm and two line segments 120 cm. According to the circumference formula of the circle, the arc length of the semicircle and the length of three line segments are calculated to calculate the circumference of the figure.
(2) Graphics can be divided into rectangle and semicircle, and the answer can be obtained by calculating the area formula of rectangle and the area formula of circle.
Solution: Solution: The circumference of the graph: 3. 14? 100? 2+ 120? 2+ 100
= 157+240+ 100
=497 (cm);
Graphic area: 120? 100+3. 14? ( 100? 2)2? 2
= 12000+3. 14? 2500? 2
= 12000+3925
= 15925 (square centimeter).
Comments: This question mainly examines the flexible application of the perimeter formula and area formula of circles and rectangles.
1 1. AB = BC = 2cm in the figure. What is the circumference of the shadow?
Analysis: According to the diagram, the circumference of the shadow part is the arc length of the big semicircle+the arc length of the two small semicircles. The answer can be calculated according to the circumference formula of a circle.
Answer: Solution: 3. 14? 2+3. 14? 2
=6.28+6.28
= 12.56 (cm),
A: The perimeter of the shadow part is 12.56 cm.
Comments: The key to solve this problem is to find the position of each semicircle where the perimeter of the shadow part is located, and then calculate it with the perimeter formula of the circle.
12. Calculate the surface area of each graph below. (Unit: cm)
Analysis: (1) According to the figure, the length, width and height of a cuboid are all 5cm, and the formula of the surface area of the cuboid is: s=(ab+ah+bh)? 2; Answer directly according to the formula;
(2) It is known that the side length of the cube is 1.5cm, and the surface area formula of the cube is: s = 6a2.
(3) According to the figure, the length, width and height of the cuboid are all 3cm, and the formula of the surface area of the cuboid is: s=(ab+ah+bh)? 2; Answer directly according to the formula.
Answer: Solution: (1)(2? 5+2? 3+5? 3)? 2
=( 10+6+ 15)? 2
=3 1? 2
=62 (square centimeter).
A: The surface area of the chart is 62 square centimeters.
(2) 1.5? 1.5? 6= 13.5 (square centimeter).
A: The surface area of the graph is13.5cm2..
(3)(3? 3+3? 4? 2)? 2
=(9+24)? 2
=33? 2
=66 (square centimeter).
A: The surface area of the diagram is 66cm2.
Comments: This topic mainly investigates the calculation method of the surface area of cuboids and cubes.