Back to Exercise: Use distance formula for area

Exercises: Compute Perimeters and Areas Using Coordinates

Show all work for each problem. Express exact answers using radical form unless a decimal
approximation is requested. Label every answer with correct units.

Grade 10·20 problems·~30 min·Common Core Math - HS Geometry·standard·hsg-gpe-b-7

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Warm-Up: Review What You Know

These problems review skills you have already learned.

What is the distance between the points $(1, 2)$ and $(4, 6)$ ?

$5$

$\sqrt{7}$

A rectangle has vertices at $A(0, 0)$ , $B(6, 0)$ , $C(6, 4)$ , and $D(0, 4)$ .
What is its area in square units?

A triangle has a horizontal base of length 8 units and a vertical height of
5 units from the base to the opposite vertex. What is its area?

40 square units

$20$ square units

13 square units

$\sqrt{89}$ square units

Fluency Practice

Apply the distance formula and area formulas to each figure.

$Right triangle with vertices A at origin, B at (5,0), and C at (5,12).$

Triangle $ABC$ has vertices $A(0, 0)$ , $B(5, 0)$ , and $C(5, 12)$ .
What is the perimeter of triangle $ABC$ ?

Quadrilateral $PQRS$ has vertices $P(0, 0)$ , $Q(4, 0)$ , $R(6, 3)$ ,
and $S(2, 3)$ . Compute the exact perimeter of $PQRS$ .

Triangle $DEF$ has vertices $D(1, 1)$ , $E(5, 1)$ , and $F(3, 4)$ .
A student says the perimeter is $4 + \sqrt{13}$ units.
What error did the student make, and what is the correct perimeter?

The student forgot side $FD$ . The correct perimeter is $4 + 2\sqrt{13}$ units.

The student computed $DE$ incorrectly. The correct perimeter is $4 + 2\sqrt{13}$ units
but for a different reason.

The student used the wrong formula. The correct perimeter is $4 + \sqrt{13}$ units.

No error was made; $4 + \sqrt{13}$ is correct.

$Tilted rectangle ABCD with vertices at (0,0), (4,2), (3,4), (-1,2).$

Rectangle $ABCD$ has vertices $A(0, 0)$ , $B(4, 2)$ , $C(3, 4)$ , and $D(-1, 2)$ .
The adjacent sides are perpendicular. What is the area of rectangle $ABCD$ ?

$Triangle PQR with horizontal base PQ at y=2 and apex R at (4,8), showing height h from R to PQ.$

Triangle $PQR$ has vertices $P(1, 2)$ , $Q(7, 2)$ , and $R(4, 8)$ .
What is the area of triangle $PQR$ ?

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