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Maksim231197 [3]
3 years ago
14

What is the area of triangle pqr on the grid? a triangle pqr is shown on a grid. the vertex p is on ordered pair 7 and 6, vertex

q is on ordered pair 1 and 6, and the vertex r is on ordered pair 4 and 2. 5 square units 6 square units 10 square units 12 square units?
Mathematics
2 answers:
aivan3 [116]3 years ago
7 0

Answer:

12

Step-by-step explanation:

horsena [70]3 years ago
6 0

P(7,6), Q(1,6), R(4,2)

We have PQ parallel to the x axis. We'll call that the base,

b = 7 - 1 = 6

The altitude is then the y difference h = 6 - 2 = 4

The area is \frac 1 2 bh = \frac 1 2 (6)(4) = 12

Answer: 12 square units


In general we can use the shoelace formula for the area of any polygon given coordinates. We write the points like this:

(7,6), (1,6), (4,2)

(1,6), (4,2), (7,6)

The area is then half the absolute value of the sum of the cross products:

A = \frac 1 2 | 7(6)-6(1) + 1(2)-6(4) + 4(6)-2(7) | = \frac 1 2 |24| = 12


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