Answer:
75 mm^2
Step-by-step explanation:
use pythageron theorem to find the area of the triangle
7^2=5^2+b^2
b=4.489mm
multiply the of b by the height (5mm) to get the area. usually for the area of a triangle you divide by two, but because there is an identical triangle on the other side, it will be doubled, so dividing it by 2 is redundant.
4.489*5 = 24.49mm^2
Make a rectangle in the middle of the shape, creating a triangle on the right, like they did on the left. That right triangle is included in the calcualtion above. the rectangle is base *height. The base is 15 - b which was 4.489. therefore the rectanlge is
5*10.1 = 50.5mm^2
add the areas together: 50.5 +24.49 = 75 mm^2
you would multiply 10 x -12 by distributing the 10 into the parenthesis.
The answer would be negative because a postive times a negative is a negative.
The answer is -120
Step-by-step explanation:
Geometry is one of the oldest branches of math. Geometry is mostly about distance, shape, size, and relative position of figures. It is related to measurement, relationships of points, lines, angles, surfaces, and solids. There are 8 types of Geometry and the basic concepts of Geometry are point, line and plane. It isn't possible to exactly define the terms, however, we know it is refers to the mark of the position and has an accurate location.
Hope this helps :)
<span>1) We are given that PA = PB, so PA ≅ PB by the definition of the radius.
</span>When you draw a perpendicular to a segment AB, you take the compass, point it at A and draw an arc of size AB, then you do the same pointing the compass on B. Point P will be one of the intersections of those two arcs. Therefore PA and PB correspond to the radii of the arcs, which were taken both equal to AB, therefore they are congruent.
2) We know that angles PCA and PCB are right angles by the definition of perpendicular.
Perpendicularity is the relation between two lines that meet at a right angle. Since we know that PC is perpendicular to AB by construction, ∠PCA and ∠PCB are right angles.
3) PC ≅ PC by the reflexive property congruence.
The reflexive property congruence states that any shape is congruent to itself.
4) So, triangle ACP is congruent to triangle BCP by HL, and AC ≅ BC by CPCTC (corresponding parts of congruent triangles are congruent).
CPCTC states that if two triangles are congruent, then all of the corresponding sides and angles are congruent. Since ΔACP ≡ ΔBCP, then the corresponding sides AC and BC are congruent.
5) Since PC is perpendicular to and bisects AB, P is on the perpendicular bisector of AB by the definition of the perpendicular bisector.
<span>The perpendicular bisector of a segment is a line that cuts the segment into two equal parts (bisector) and that forms with the segment a right angle (perpendicular). Any point on the perpendicular bisector has the same distance from the segment's extremities. PC has exactly the characteristics of a perpendicular bisector of AB. </span>
