Question

PLs, help me with this question

Answer 1

See below.

Explanation:

Perimeter: use the Distance Formula
`d=√((x_2-x_1)^2+(y_2-y_1)^2)`

Distance from (-3, 4) to (4, 5) is

`√((5-4)^2+(4-(-3))^2)=√(1+49)=√(50)=5√(2)`

Distance from (4, 5) to (2, -3) is

`√((2-4)^2+(-3-5)^2)=√(4+64)=√(68)=2√(17)`

Distance from (2, -3) to (-4, 4) is

`√((-4-2)^2+(-4-(-3)))=√(36+1)=√(37)`

Distance from (-4, 4) to (-3, 4) is

`√((-4-(-3))^2+(4-(-4))^2)=√(1+64)=√(65)`

The perimeter is the sum of all these distances.

Area:

To find the area of the figure, one method is to draw a rectangle around the entire figure, then add line segments that cut up the unwanted area into rectangles and triangles, add those areas together, then subtract the total from the area of the surrounding rectangle. See the attached figure.

The surrounding rectangle has area 8 x 9 = 72 square units.

The unwanted areas (green rectangles and four triangles). Remember, the area of a triangle is (1/2)(length)(width).

Rectangle A: 1 x 1 = 1 square unit

Triangle B: (1/2)(7)(1) = 3.5 square units

Triangle C: (1/2)(8)(1) = 4 square units

Triangle D: (1/2)(8)(2) = 8 square units

Triangle E: (1/2)(6)(1) = 3 square units

Rectangle F: 2 x 1 = 2 square units

Total of unwanted area: 1 + 3.5 + 4 + 8 + 3 + 2 = 21.5 square units

Subtract this total from the surrounding rectangle's area to get

72 - 21.5 = 50.5 square units