What Shape Am I?
I am a quadrilateral where my diagonals bisect each other, but they are not necessarily equal in length or perpendicular.
Parallelogram
The ratio of the angles in a triangle is 1:2:3. What is the measure of each angle, and what type of triangle is it?
30 degrees, 60 degrees, 90 degrees (right triangle)
A rectangle has a length of 10 cm and a diagonal of 26 cm. What is the area of the rectangle?
240 cm²
A rectangle has an area of 48 cm² and a width of 6 cm. What is its perimeter?
28 cm
Sarah wants to build a rectangular pen for her rabbit that has an area of 24 square feet. If she wants to use the least amount of fencing, what should the dimensions of the pen be, and what is the perimeter?
4 feet by 6 feet, with a perimeter of 20 feet
I am a triangle containing one angle that is exactly twice the measure of one of the other acute angles.
Isosceles triangle or a right triangle
In an isosceles triangle, the measure of the vertex angle is 40 degrees. What is the measure of each base angle?
70 degrees
A rhombus has a perimeter of 40 cm and one diagonal of 12 cm. What is the area of the rhombus?
96 cm²
A square has a diagonal of 10√2 meters. What is its perimeter?
40 meters
A triangular garden needs to be covered with mulch. The sides of the garden are 5 meters, 12 meters, and 13 meters. If one bag of mulch covers 10 square meters, how many bags will Sarah need?
3 bags
I am a quadrilateral with exactly one pair of parallel sides, and the other sides are not parallel but do have the same length.
Isosceles trapezium
One of the exterior angles of a triangle measures 110 degrees. The interior opposite angles are in the ratio 2:3. Find the measures of these two interior angles.
44 degrees and 66 degrees
A parallelogram has a base of 15 m and a side adjacent to the base of 8 m. If the height of the parallelogram with respect to the base is 6 m, what is the area of the parallelogram?
90 m²
A right triangle has legs of 5 cm and 12 cm. What is its perimeter?
30 cm
A window is shaped like a trapezium with parallel sides of 1.5 meters and 2.5 meters and a height of 1 meter. If the cost of glass is $15 per square meter, what is the cost of the glass for the window?
$30
I am a quadrilateral where all four sides are congruent, and my diagonals are perpendicular bisectors of each other. I have 2 answers.
Rhombus and square
A right triangle has acute angles whose measures are (2x + 5) degrees and (3x - 10) degrees. Find the value of x and the measure of each acute angle.
x = 19, angles are 43 degrees and 47 degrees
A trapezium has parallel sides of 8 cm and 12 cm and a height of 5 cm. If a square section with a side length of 2 cm is removed from the center, what is the remaining area of the trapezium?
46 cm²
A parallelogram has an area of 72 m² and a height of 9 m. If one of the sides adjacent to the base is 10 m, what is the perimeter?
36 m
A park is shaped like a parallelogram with a base of 50 meters and a height of 30 meters. A rectangular section of 10 meters by 20 meters is used for a playground. What is the remaining area of the park?
1300 m²
I am a quadrilateral with two pairs of adjacent sides that are equal in length. My diagonals intersect at right angles, but they do not bisect each other.
Kite
An equilateral triangle is divided into two congruent right triangles by drawing an altitude. If the side length of the equilateral triangle is 10 cm, what are the measures of the angles in each right triangle?
90 degrees, 60 degrees, 30 degrees
A kite has diagonals of 10 cm and 24 cm. A square with the same area as the kite is created. What is the side length of the square?
√120 cm (approximately 10.95 cm)
A rhombus has an area of 96 cm² and one diagonal of 16 cm. What is its perimeter?
40 cm
A kite-shaped banner has diagonals of 1 meter and 1.5 meters. If the material for the banner costs $10 per square meter, what is the cost of the material for 5 such banners?
$37.50