Question

use the picture to the right to answer questions 8 – 10.

1. what is the perimeter of the composite figure?

a. 40 units
b. 102.5 units
c. 110 units
d. 4583 units

1. what is the area of the composite figure?

a. 102.5 units²
b. 110 units²
c. 95 units²
d. 4583 units²

1. a student used his compass to construct (overline{be}), the bisector of (angle abc). how could he make sure that it is accurate?

a. he found that two points intersect at ( f ).
b. he must place their compass on points ( d ) and ( e ).
c. he must place their compass on ( b ) and drew both arcs.
d. he fixed their compass on ( b ) and drew both arcs.

1. a student was attempting to construct the perpendicular bisector of (overline{ab}). which of the statements below describes what the student may have done wrong?

a. they didn’t do anything wrong. they need to connect the opposite endpoints to finish.
b. on the second step, they should have placed the compass point just where the first arc intersects (overline{ab}).
c. they just needed to open the compass more to make arcs that have a radius more than half the length of (overline{ab}).
d. they should have started by placing the compass point at the midpoint of (overline{ab}).

1. what construction is shown?

a. angle bisector
b. perpendicular bisector
c. parallel lines
d. congruent segments

Explanation:

Questions 8-9

Step1: Count grid sides for perimeter

Assume each grid square has side length 1 unit. Trace the composite figure's outer edges: count horizontal and vertical segments. The outer perimeter totals 40 units.

Step2: Count full/half grids for area

Count full grid squares: 95 full squares. There are no partial squares to add, so area = 95 units².

To construct angle bisector $\overrightarrow{BD}$ of $\angle ABC$, the standard method is to first place the compass on vertex $B$, draw arcs that intersect both sides $BA$ and $BC$ (points $E$ and $F$).

When constructing a perpendicular bisector of $\overline{AB}$, after drawing arcs from $A$ and $B$, the next step is to set the compass to a radius more than half the length of $\overline{AB}$ (already done), then draw intersecting arcs from the two initial arc intersections. The student's error is not recognizing they only need to connect the intersecting arc points to finish.

Answer:

1. A. 40 units
2. C. 95 units²

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Question 10