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Authoritative PPT Summary
"Polygons in Life" PPT courseware 3
Review 1: Find the area of the following figure:
Area of parallelogram = base × height
= 20 × 8
=160 (square centimeters)
Area of rectangle = length × width
= 12×4.5
= 54 (square decimeters)
area of square
= side length × side length
= 8 × 8
64 (square meters)
Review 2:
Find the height of the base of the triangle below:
Exploration 1:
Two identical acute-angled triangles can be assembled into a parallelogram by rotation and translation.
The base of the parallelogram is equal to the base of the triangle, and the height is equal to the height of the triangle.
Two identical acute-angled triangles can be combined to form a parallelogram.
Exploration 2:
Two identical right triangles can be combined into a parallelogram (rectangle) by rotation and translation.
The base of the parallelogram is equal to the base of the triangle, and the height is equal to the height of the triangle.
Exploration three:
Two identical obtuse triangles can be assembled into a parallelogram by rotation and translation.
The base of the parallelogram is equal to the base of the triangle, and the height is equal to the height of the triangle.
summary:
Two identical arbitrary triangles can be assembled into a parallelogram through rotation and translation; the base of the parallelogram is equal to the base of the triangle, and the height is equal to the height of the triangle. The area of a parallelogram is equal to twice the area of a triangle.
Because: area of triangle = area of parallelogram ÷ 2
= base × height ÷ 2
So: Area of triangle = Base × Height ÷ 2
S = ah÷2
Improvement exercises:
1. Judgment
1. Two right triangles can definitely form a rectangle. ( )
2. The area of a parallelogram is equal to twice the area of a triangle. ( )
3. Triangles with equal bases and equal heights have equal areas, but not necessarily the same shapes. ( )
2. Find the area of the following figure:
S = 15×8÷2= 60 (square centimeters)
3. The three sides of a right triangle are 3, 4, and 5 cm long respectively. What is the area of this triangle in square centimeters?
Ｓ＝ah÷2
= 3×4÷2
= 6 (square centimeters)
Answer: The area of this triangle is 6 square centimeters
Expansion exercises:
Fill in the blanks:
1. The area of two triangles with equal bases and equal heights ( ).
2. The area of a triangle with equal bases and equal heights is the area of a parallelogram ( ).
3. The base area of the triangle is 25 square meters, and the area of the parallelogram with the same base and height is ( ).
2. Find X of the following figure
7X÷2＝21
Solution: 7X=42
Ｘ＝６
5X÷2＝3×4÷2
Solution: 5X=12
Ｘ＝2.4
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"Polygons in Life" PPT courseware 4:
"Polygons in Life" PPT courseware 4 The area of a trapezoid Review the method of deriving the area of a triangle Because: S=ah So: S=ah2 What did you find? A rectangle can be cut into two trapezoids along a straight line. A parallelogram can be cut into two along a straight line..
"Polygons in Life" PPT courseware 2:
"Polygons in Life" PPT courseware 2 The area of a rectangle = length X width The area of a square = side length X side length What is a parallelogram? Indicate its base and height. Characteristics of a parallelogram ① Opposite sides are parallel and equal ② Opposite angles are equal ... ... ... Parallelogram...
"Polygons in Life" PPT courseware:
"Polygons in Life" PPT courseware This unit reviews the key points of the area formula and its application, the derivation of the area formula, the conversion of area units, the development of spatial concepts, and the solution of practical problems. The area of a rectangle = the area of a square with length and width = the area of a parallelogram with long sides and long sides. .