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2.7 kmuv11.2 km4.1 km12.3 km

User Pbk
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1 Answer

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To make the explanation easy to understand I've named all points of the shape.

You have the sides:

AB= 12.3 km

BC= 4.1 km

EF= 2.7 km

FA= 11.2 km

First stem is calculating u and v

u= ED

As you can see in the graphic, the length of the line FA is the same as adding the lines BC and ED

FA= BC + ED

So to know how much is ED you have to subtract BC from FA

u= ED= FA - BC= 11.2 - 4.1= 7.1 km

v= CD

To calculate CD you have to use the lines AB and EF, as you can see the lenght of AB is the same as de total lenght of CD and EF:

AB= CD + EF

Then,

v= CD= AB - EF= 12.3 - 2.7= 9.6 km

So u= 7.1 km and v= 9.6 km

Next are the perimeter and area of the shape. To calculate both of them you have to divide the figure into two simplear ones.

You can see I've added a purple line GD and created a rectangle ABCG and a rectangle DEFG so that you can calculate the area and permimeter of both figures and them add them to have to total area and permimeter of the figure.

Perimeter (P)

Rectangle DEFG

The perimeter of a rectangle (P1) is equal to the sum of all its sides.

As you can see EF= GD and DE=FG

P1= DE + EF + FG + GD= 2*EF + 2*FG= 2*7.1+2*2.7= 19.6 km

Rectangle ABCG

P2= 2*AB + 2*BC= 2*12.3+2*4.1= 32.8km

Next you add the permimeters of both rectangles to have the permimeter of the figure

P= P1 + P2= 19.6 + 32.8= 52.4 km

The permimeter of the figure is 52.4 km.

One hectometer is equal to 100m, is a unit that expreses the distance in "hundreds of meters"

The kilmeter is equal to 1000m, meaning it shows distance in thousands of meters.

To convert units from km to hm you have to mulyiply them by 10 (or move the coma one dcimal unit to the right)

So 52.4km *10= 524hm

Area

The area of a rectangle is equal to the base (b) by the height (h) of the rectangle.

Rectangle DEFG

For this rectangle the base is b1= EF= 2.7 km and the height is h1= DE= 7.1 km

So the area is

A1= b1*h1= 2.7*7.1= 19.17 km²

Note: since the calculation we did multiplies km*km the resulting unit will be square km: km²

Rectangle ABCG

Base b2= AB= 12.3 km

Height h2= BC= 4.1 km

Area A2= b2*h2= 12.3 * 4.1= 50.43 km²

Total area:

A= A1 + A2= 19.17 + 50.43= 70.13 km²

Now to convert this is not as simple beause these are square units.

Rembember that 1 km² = 100hm²

So to convert 70.13km² to hm² you have to multiply it by 100

70.13*100= 7013hm²

So:

u= 7.1km

v= 9.6km

Perimeter

52.4 km

524 hm

Area

70.13 km²

7013 hm²

2.7 kmuv11.2 km4.1 km12.3 km-example-1
User Szymon Maszke
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