Geometrymath Problem Solving

Solve the above quadratic equation for W and substitute to find L W = 3 and L + 6 Let r be the radius of the disk. Area is known and equal to 100π; hence 100π = π r 2 Solve for r: r = 10 Circumference = 2 π r = 20 π Let r be the radius of the semicircle. Area of the semicircle is known; hence. Guideline to follow while using the free math problem solver. As you enter your math problems, the solver will show you the Math Format automatically to make sure you have effectively entered the math problem you really want it to solve. You cannot enter word problems since the.

Ladder
4 m long ladder touches the cube 1mx1m at the wall. How high reach on the wall?
Angle of the body diagonals
Using vector dot product calculate the angle of the body diagonals of the cube.
Center
Calculate the coordinates of the circle center: ?
Vector
Determine coordinates of the vector u=CD if C[19;-7], D[-16,-5].
Cone
If the segment of the line y = -3x +4 that lies in quadrant I is rotated about the y-axis, a cone is formed. What is the volume of the cone?
Find the 12
Find the equation of the circle with center (3,7) and circumference 8π units.
Angle between lines
Calculate the angle between these two lines: ? ?
Perpendicular
Determine the slope of the line perpendicular to the line p: y = -x +4.
Distance
Wha is the distance between the origin and the point (18; 22)?
Coordinates of vector
Determine the coordinate of a vector u=CD if C(19;-7) and D(-16;-5)
Points collinear
Show that the point A(-1,3), B(3,2), C(11,0) are col-linear.
Segment
Calculate the segment AB's length if the coordinates of the end vertices are A[10, -4] and B[5, 5].
Distance
Calculate distance between two points X[18; 19] and W[20; 3].
Distance problem
A=(x, x) B=(1,4) Distance AB=√5, find x;
Calculate 8
Calculate the coordinates of point B axially symmetrical with point A[-1, -3] along a straight line p : x + y - 2 = 0.
Linear independence
Determine if vectors u=(-4; -5) and v=(20; 25) are linear Linear dependent.
Sphere equation
Obtain the equation of sphere its centre on the line 3x+2z=0=4x-5y and passes through the points (0,-2,-4) and (2,-1,1).
Line
Line p passing through A[-10, 6] and has direction vector v=(3, 2). Is point B[7, 30] on the line p?
Circle - AG
Find the coordinates of circle and its diameter if its equation is: ?
Forces
In point O acts three orthogonal forces: F₁ = 20 N, F₂ = 7 N, and F₃ = 19 N. Determine the resultant of F and the angles between F and forces F₁, F₂, and F₃.

A variety of geometry word problems along with step by step solutions will help you practice lots of skills in geometry.
Word problem #1:
The measure of one supplementary angle is twice the measure of the second. What is the measure of each angle?
Let x be the measure of the first angle. Then, the second angle is 2x.
Since the angle are supplementary, they add up to 180°
x + 2x = 180°
3x = 180°
Since 3 × 60 = 180, x = 60
The measure of the first angle is 60°
The measure of the second is 2x = 2 × 60 = 120°
Word problem #2:
Without plotting the points, say if the points (2, 4), (2, 0), and (2, -6) are colinear.
If the x-coordinate or the y-coordinate is the same for all points, then the points are colinear.
After a close inspection, we see that the x-coordinate is the same for all points. Therefore, the points are colinear.
Word problem #3:
The perimeter of a square is 8 cm. What is the area?
If the perimeter is 8 cm, then the length of one side is 2 cm since 2 cm + 2 cm + 2 cm + 2 cm = 8 cm.
Area = 2 cm × 2 cm = 4 cm².
Word problem #4:
A right triangle has acute angles whose measures are in the ratio 1:3
Find the measure of these acute angles.
$Geometrymath Problem Solving$ Thing to know: The sum of the angles in a triangle is equal to 180°
Meaning of the ratio 1:3
This means that the second acute angle is 3 times bigger than the first acute angle.
Let x be the first acute angle, then the second acute angle will be 3x.
x + 3x + 90° = 180°
4x + 90° = 180°
4x + 90° - 90° = 180° - 90°
4x = 90°
Since 4 × 22.5 = 90°, x = 22.5°
The second angle is 3x = 3 × 22.5 = 67.5
The measure of the two acute angles are 22.5 and 67.5

Tricky and interesting geometry word problems

Word problem #5:
The midpoint of a segment is (3, 6). If one endpoint is (4, 7), what is the other endpoint?
Suppose x₁ is the missing x-coordinate of the other endpoint.
To get the x-coordinate of the midpoint, you will need to do the math below:

= 3

x₁ = 2 since 2 + 4 = 6 and 6 divided by 2 = 3

Suppose y₁ is the missing y-coordinate of the other endpoint.
To get the y-coordinate of the midpoint, you will need to do the math below:

= 6

y₁ = 5 since 5 + 7 = 12 and 12 divided by 2 = 6
The other endpoint is (2, 5)
Word problem #6:
The sum of the measures of the angles of an n-gon is 2340°. How many sides does this n-gon have?
To solve this problem, you need to know the following formula:
Sum of the angles in an n-gon = (n - 2)× 180°
n is the number of sides. So just plug in the numbers and solve.
2340° = (n - 2)× 180°
2340° = 180°n - 360°
2340° + 360° = 180°n - 360° + 360°
2700° = 180°n
Divide both sides 180°
(2700° ÷ 180°) = (180° ÷ 180°)n
15 = n
The n-gon has 15 sides
Word problem #7:
If two lines are perpendicular, what is the slope of the first line if the second line has a slope of 5.
When two lines are perpendicular, the following equation is true
Let m₁ × m₂ = -1
m₁ is the slope of the first line and m₂ is the slope of the second line
Thus, m₁ × 5 = -1
Divide both sides of this equation by 5

(m₁ × 5 ÷ 5) = (-1 ÷ 5)

m₁ = = - 0.20

Word problem #8:
The diameter of a penny is 0.750 inch and the diameter of a quarter is 0.955 inch.
You put the penny on top and exactly in the middle of the quarter. Since the coin is smaller, it will not cover completely the quarter.

What is the area of the portion that is not covered? Will the area change if the coin is not centered?
We can use A = πr² since the coin is shaped like a circle.
Let B stand for the area of the portion not covered.
B = area of quarter - area of penny
r = 0.375 inch for the penny and r = 0.4775 for the quarter
B = 3.14 × 0.4775 × 0.4775 - 3.14 × 0.375 × 0.375
B = 0.715 - 0.441
B = 0.274 inch²
As long as the coin remains inside the quarter, the area that is not covered should stay the same.

Want more geometry word problems? Check the ebook below

The ebook above will show you how to solve many more geometry word problems as you explore some important geometric formulas.

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