Question

Determine what shape is formed for the given coordinates for ABCD, and then find the perimeter and area as an exact value and rounded to the nearest tenth. A (−10, 5), B (−7, 1), C (1, 7), D (−6, 8)

Answer 1

Perimeter = 27 units

Area = 37.5 sq. units

Explanation:

We have to find the length of all the sides to determine what kind of quadrilateral this is.

Length of AB =
`\sqrt{(-10+7)^(2)+(5-1)^(2)} = √(9+16) =√(25)= 5`

Length of BC =
`\sqrt{8^(2)+6^(2)} = 10`

Length of CD =
`\sqrt{7^(2)+1^(2)}` = 5
`√(2)`

Length of DA =
`\sqrt{4^(2)+3^(2)}`= 5

The shape is a quadrilateral.

To find the perimeter sum the length of all the sides,

PERIMETER = 5+10+5
`√(2)`+5 =27 units

We can find area by finding areas of triangles separately.

Area of ΔABC = 25 sq. units

Area of ΔACD = 12.5 sq. units

Area of quadrilateral= 25 + 12.5 = 37.5 sq. units