Question

Determine whether the triangle or the rectangle has a greater area. Which one has a greater perimeter?Make calculations to justify yourreasoning.

Answer 1

Step-by-step explanation

We are told to compare the perimeters of the two figures given, and then determine the greater one,

To do so, we will have to split the trapezoid into two: A rectangle and A triangle as shown in the image below

Figure A is a triangle

Figure B is a rectangle

To get the perimeter, we will add the exteriors of all the sides

So we can compute the perimeter as follows

Figure A

We need to obtain x using the Pythagoras theorem

`\begin{gathered} x^2=4^2+6^2 \\ x=√(16+36) \\ x=√(52) \\ x=2√(13) \\ x=7.211 \end{gathered}`

Therefore, the perimeter of the triangle is

`7.211+4+6=17.211`

The area of the triangle is

`Area\text{ of triangle =}(1)/(2)* base* height=(1)/(2)*6*4=12\text{ square units}`

Then for figure B which is a rectangle

The perimeter of the rectangle is

`4+6+4+6=20`

Therefore, the perimeter of the triangle is 20 units

The area of the rectangle is

`area\text{ = length}* breadth=4*6=24\text{ square units}`

Since 20 is greater than 17.211, we can conclude that

The perimeter of the rectangle is greater than the triangle

Also comparing the area, since 24 square units are greater than 12 square units, the area of the rectangle is greater than the triangle.

so in both cases, the perimeter and area of the rectangle are greater than the triangle