Question

calcule le périmètre et laire des figures ci - contre. complète ensuite les énoncés. à laide du clavier, écris le nombre ou le terme approprié dans chaque case.
a) le trapèze a un périmètre de cm et une aire de cm²?
b) le losange a un périmètre de cm et une aire de cm²?
c) parmi ces deux figures, le a le plus petit périmètre.
d) parmi ces deux figures, le a la plus petite aire.

Explanation:

a) Trapeze (Trapèze)

Step 1: Calculate the perimeter of the trapezoid

A trapezoid has four sides: the two bases and the two legs. From the diagram, the lengths are \( 2.8 \, \text{cm} \), \( 4.6 \, \text{cm} \), \( 2.2 \, \text{cm} \), and \( 2.2 \, \text{cm} \) (assuming the non - parallel sides are equal? Wait, no, looking at the trapezoid: the two parallel sides (bases) are \( 2.8 \, \text{cm} \) and \( 4.6 \, \text{cm} \), and the two non - parallel sides (legs) are both \( 2.2 \, \text{cm} \)? Wait, no, maybe I misread. Wait, the trapezoid: let's check the sides. The perimeter \( P \) of a trapezoid is the sum of all its sides. So \( P=2.8 + 4.6+2.2 + 2.2\)
\(P=(2.8 + 4.6)+(2.2 + 2.2)=7.4 + 4.4 = 11.8\,\text{cm}\)

Step 2: Calculate the area of the trapezoid

The formula for the area of a trapezoid is \( A=\frac{(a + b)}{2}\times h\), where \( a \) and \( b \) are the lengths of the two parallel sides (bases) and \( h \) is the height. Here, \( a = 2.8\,\text{cm} \), \( b = 4.6\,\text{cm} \), and \( h = 2\,\text{cm} \) (the height is given as \( 2\,\text{cm} \)).
\(A=\frac{(2.8 + 4.6)}{2}\times2=(2.8 + 4.6)\times1=7.4\,\text{cm}^2\)

b) Rhombus (Losange)

Step 1: Calculate the perimeter of the rhombus

A rhombus has four equal - length sides. From the diagram, the diagonals are \( d_1 = 4\,\text{cm} \) and \( d_2 = 2\,\text{cm} \)? Wait, no, to find the side length of a rhombus, we can use the fact that the diagonals of a rhombus bisect each other at right angles. So if the diagonals are \( d_1 = 4\,\text{cm} \) and \( d_2 = 2\,\text{cm} \), then half of each diagonal is \( \frac{d_1}{2}=2\,\text{cm} \) and \( \frac{d_2}{2} = 1\,\text{cm} \). Then the side length \( s\) of the rhombus is given by the Pythagorean theorem \( s=\sqrt{(\frac{d_1}{2})^2+(\frac{d_2}{2})^2}=\sqrt{2^2 + 1^2}=\sqrt{4 + 1}=\sqrt{5}\approx2.24\,\text{cm} \). But wait, maybe the rhombus has side length \( 2.25\,\text{cm} \) (from the diagram, there is a \( 2.25\,\text{cm} \) mark). Wait, if the side length of the rhombus is \( 2.25\,\text{cm} \), then the perimeter \( P = 4\times s=4\times2.25 = 9\,\text{cm} \)

Step 2: Calculate the area of the rhombus

The formula for the area of a rhombus is \( A=\frac{d_1\times d_2}{2} \), where \( d_1 \) and \( d_2 \) are the lengths of the diagonals. If \( d_1 = 4\,\text{cm} \) and \( d_2 = 2\,\text{cm} \), then \( A=\frac{4\times2}{2}=4\,\text{cm}^2 \)

c) Compare perimeters

The perimeter of the trapezoid is \( 11.8\,\text{cm} \) and the perimeter of the rhombus is \( 9\,\text{cm} \). So the rhombus (losange) has the smaller perimeter.

d) Compare areas

The area of the trapezoid is \( 7.4\,\text{cm}^2 \) and the area of the rhombus is \( 4\,\text{cm}^2 \). So the rhombus (losange) has the smaller area.

Answer:

s:
a) Perimeter: \( 11.8\,\text{cm} \), Area: \( 7.4\,\text{cm}^2 \)

b) Perimeter: \( 9\,\text{cm} \), Area: \( 4\,\text{cm}^2 \)

c) Le losange (the rhombus)

d) Le losange (the rhombus)