Question

Draw and classify the polygon with the given vertices. Find the perimeter and the area of the polygon. M(-2,5), N(3,-2), P(-2,-2)

Answer 1

Perimeter = 20.6cm to 1dp = 20.60cm to 2dp

Area = Base = 8.6/2 = 4.3 x 4.069 = 17.5cm^2

Height is found 4.07 cos( 54.47deg) 5/8.6 = 4.069cm

Explanation:

Right angle side triangle, sides

= MN =8.6cm

= NP=5cm

= PM=7cm

= 25sq + 49sq = 74sq

MN^2 =√74 = 8.60232526704 = 8.6cm

P = 8.6 + 5 + 7 = 20.6cm

Answer 2

• see below for a drawing
• right triangle
• perimeter = 20.6 units
• area = 17.5 units²

Explanation:

A graph shows the figure to be a right triangle with a base of 5 units and a height of 7 units. Its hypotenuse will be given by the Pythagorean theorem:

MN² = MP² +PN²

MN² = 7² +5² = 74

MN = √74 ≈ 8.60

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The perimeter is the sum of the side lengths:

Perimeter = MN +MP +PN = 8.60 +7 +5

Perimeter = 20.60 . . . . units

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The area is given by the area formula:

Area = 1/2bh = 1/2·5·7 = 35/2

Area = 17.5 . . . . square units

The polygon is a right triangle with a perimeter of 20.60 units and an area of 17.5 square units