ISEE Middle Level Quantitative : Plane Geometry
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Example Questions
Example Question #241 : Plane Geometry
Note: Figure NOT drawn to scale.
Refer to the above triangle. An insect walks directly from A to B, then directly from B to C. What fraction of the perimeter of the triangle has he walked?
By the Pythagorean Theorem, the distance from A to C, which we will call 
The perimeter of the triangle is 
Example Question #11 : Triangles
Note: Figure NOT drawn to scale
Refer to the above triangle. An insect walks directly from B to C, then directly from C to A. What fraction of the perimeter of the triangle has he walked?
By the Pythagorean Theorem, the distance from B to C, which we will call 
The perimeter of the triangle is
The insect has traveled 
of the perimeter.
Example Question #243 : Plane Geometry
Note: Figure NOT drawn to scale
Refer to the above triangle. An insect walks directly from A to B, then directly from B to C. What percent of the perimeter of the triangle has he walked?
By the Pythagorean Theorem, the distance from B to C, which we will call
The perimeter of the triangle is
The insect has traveled 
Example Question #1 : How To Find The Area Of A Triangle
A triangle has base 80 inches and area 4,200 square inches. What is its height?
Use the area formula for a triangle, setting 
Example Question #1 : How To Find The Area Of A Triangle
The sum of the lengths of the legs of an isosceles right triangle is one meter. What is its area in square centimeters?
It is impossible to determine the area from the information given
The legs of an isosceles right triangle have equal length, so, if the sum of their lengths is one meter, which is equal to 100 centimeters, each leg measures half of this, or
The area of a triangle is half the product of its height and base; for a right triangle, the legs serve as height and base, so the area of the triangle is
Example Question #11 : Triangles
The above figure depicts Square 
Since 
The area of 
The area of the square is the square of the length of a side, which is 
Example Question #2 : How To Find The Area Of A Triangle
Which of the following is the greater quantity?
(a) The area of the above triangle
(b) 800
(a) and (b) are equal
It is impossible to determine which is greater from the information given
(b) is the greater quantity
(a) is the greater quantity
(b) is the greater quantity
The area of a right triangle is half the product of the lengths of its legs, which here are 25 and 60. So
which is less than 800.
Example Question #2 : How To Find The Area Of A Triangle
The above figure gives the lengths of the three sides of the triangle in feet. Give its area in square inches.
The area of a right triangle is half the product of the lengths of its legs, which here are 
Multiply each length by 12 to convert to inches - the lengths become 
Example Question #245 : Plane Geometry
Figure NOT drawn to scale
Square 
(a) The area of
(b) The area of
(a) and (b) are equal
It is impossible to determine which is greater from the information given
(a) is the greater quantity
(b) is the greater quantity
(b) is the greater quantity
Square 
Since 
Therefore, 
Since 
and
Example Question #4 : How To Find The Area Of A Triangle
Figure NOT drawn to scale.
In the above diagram, Square 
(a) The area of
(b) The area of
(a) is the greater quantity
It is impossible to determine which is greater from the information given
(a) and (b) are equal
(b) is the greater quantity
(b) is the greater quantity
Square 
The area of a right triangle is half the product of the lengths of its legs.
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