ANSWERS:
BONUS QUESTION
 HELD ON MAY 6 and 7, RESULTS ON MAY 11, 2018
MAY 11, 2018
MULTIPLE CHOICE
1.
2.
3.
4.
5.
B
D
C
C
C
ESSAY
6. THE RELATIONSHIP BETWEEN THE SIDES AND ANGLES OF NONRIGHT TRIANGLE IS THE LAW OF SINES, AND WE KNOW THAT DIFFERENT
TRIANGLES HAVE DIFFERENT ANGLES AND SIDE LENGTHS, BUT ONE THING IS
FIXED, THAT EACH TRIANGLE IS COMPOSED OF THREE INTERIOR ANGLES AND
THREE SIDES THAT CAN BE OF THE SAME LENGTH OR DIFFERENT LENGTHS.
7.
 GENERAL EQUATION: A = ½bh WHERE B IS THE BASE AND H IS THE
HEIGHT OF THE TRIANGLE.
Example:
Find The Area of The Triangle.
The Area (A) Of A Triangle Is Given by The Formula A=12BH A=12BH Where (B) Is the
Base And (H) Is the Height of The Triangle.
Substitute 14 For B And 10 For H In the Formula.
A=12(14)(10) A=12(14)(10)
Simplify.
A=12(140) =70A=12(140) =70
The Area of The Triangle Is 7070 Square Meters.
 SCISSORS METHOD: A = ½ab sin(θ) if given two sides with angle in
between.
Example 1:
Find the area of ΔPQRΔPQR.
You have the lengths of two sides and the measure of the included angle.
So, you can use the formula R=12pr sin(Q) R=12pr sin(Q) where p and r are
the lengths of the sides opposite to the vertices P and R respectively.
Using the formula, the area, R=12(3)(4) sin (145°) R=12(3)(4) sin (145°).
Simplify.
R=6sin (145°) ≈6(0.5736) ≈3.44R=6sin (145°) ≈6(0.5736) ≈3.44
Therefore, the area of ΔPQRΔPQR is about 3.443.44 sq.cm.

HERON’S FORMULA: Area = √s (s - a) (s - b) (s - c)
FOR FINDING THE AREA OF A TRIANGLE IN TERMS OF THE LENGTHS OF ITS
SIDES. IN SYMBOLS, IF A, B, AND C ARE THE LENGTHS OF THE SIDES
Example
Three sides of a given triangle are 8 units, 11 units, and 13 units.
Find its semi-perimeter and its area.
Solution
the formula that is used to find the area of a triangle with 3 sides is,
Area =√[s(s-a) (s-b) (s-c)], where 'a', 'b', 'c' are the three sides and 's'
is the semi perimeter of the triangle. In this case, a = 8; b = 11, c =
13, and the semi-perimeter is, s = 8 + 11 + 13 = 32/2 = 16
Let us calculate the area of a triangle with 3 sides, using Heron's
formula.
A =√[s(s-a) (s-b) (s-c)]
= √ [16(16-8) (16-11) (16-13)]
= √ [16 × 8 × 5 × 3]
= √16 × √8 × √5 × √3
= 4 × 2√2 × √5 ×√3
= 8 √30 = 43.817 unit2
Area of the given triangle = 43.817 unit2
8. IN THREE DIMENSIONS, LIKE A CUBE, A SPHERE, OR A PYRAMID,
THE SURFACES CAN'T ALL BE SEEN AT ONE TIME. TOTAL SURFACE
AREA IN THAT CASE MEANS ADDING UP THE AREAS OF ALL THE
SURFACES. FOR A CUBE, THAT MEANS ADDING UP THE SURFACE
AREA OF ALL SIX SIDES. FOR A SPHERE LIKE A BASEBALL, YOU WANT
TO KNOW HOW MUCH AREA THE LEATHER CASING MEASURED.