6.01 Area of special quadrilaterals
For the following parallelogram:
If the parallelogram is formed into a rectangle, find:
The length of the rectangle.
The width of the rectangle.
Find the area of the parallelogram.
The given parallelogram is formed into a rectangle:
Find the area of the rectangle.
Find the area of the parallelogram.
Find the area of the following parallelogram by rearranging it into a rectangle:
Find the area of the following parallelograms:
Find the area of the parallelograms with the following dimensions:
The base is 5\text{ in}, and the perpendicular height is 2\text{ in}.
The base is 15\text{ ft} and the perpendicular height is 7\text{ ft}.
Find the value of b or h in the following parallelograms:
Area =36\text{ ft}^2
Area =35\text{ yd}^2
Find the base length of a parallelogram whose area is 108\text{ in}^2 and perpendicular height is 9\text{ in}.
Find the perpendicular height of a parallelogram whose area is 99\text{ yd}^2 and base is 9\text{ yd}.
Determine whether the following could be the dimensions of a parallelogram with an area of 28\text{ in}^2:
Base =1\text{ in}, height =28\text{ in}
Base =7\text{ in}, height =4\text{ in}
Base =4\text{ in}, height =7\text{ in}
Base =2\text{ in}, height =28\text{ in}
Complete the following table of base and height measurements for different parallelograms with an area of 60\text{ cm}^2:
| \text{Base (cm)} | 10 | 30 | |
|---|---|---|---|
| \text{Height (cm)} | 12 | ||
| \text{Area (cm}^2) | 60 | 60 | 60 |
The given trapezoid is split into a rectangle and a right-angled triangle:
Find the area of the rectangle.
Find the area of the triangle.
Find the area of the trapezoid.
For each of the folowing parallelograms made from two identical trapezoids:
Find the area of the entire parallelogram.
Find the area of one of the trapezoids.
Consider the two identical trapezoids that are used to make the following rectangle:
Find the area of the entire rectangle.
Find the area of one of the trapezoids.
The given trapezoid is formed into a rectangle:
Find the length, l, of the rectangle.
Find the area of the trapezoid.
Find the area of the following trapezoids:
The given rhombus can be split into two triangles:
Find the area of one triangle.
Find the area of the rhombus.
The given rhombus, with diagonal lengths x and y, is formed into a rectangle:
Find the length of the rectangle in terms of x and/or y.
Find the height of the rectangle x and/or y.
Now, state the formula for the area of the rhombus.
Find the area of the following rhombuses:
Determine whether the following pairs of values could be the diagonal lengths, x and y of a rhombus with an area of 9 \,\text{in}^2:
x = 2 \,\text{in} and y = 9 \,\text{in}.
x = 6 \,\text{in} and y = 3 \,\text{in}.
x = 12 \,\text{in} and y = 3 \,\text{in}.
x = 6 \,\text{in} and y = 6 \,\text{in}.
The given kite can be split into two triangles:
Find the area of one of the triangles.
Find the area of the kite.
The given kite is formed into a rectangle:
Find the length of the rectangle.
Find the width of the rectangle.
Find the area of the kite.
Find the area of the following kites:
A harbor has a trapezoidal pier with a perpendicular height of 8 \text{ yd}. One base of the pier has a length of 9 \text{ yd} and the other has a length of 5 \text{ yd}.
Find the area of the pier.
Some car parks require the cars to park at an angle as shown. The dimensions of the car park are as given, where each individual parking space has a length of 5.1\text{ m} and a width of 3.9\text{ m}. What area is needed to create an angled car park suitable for 7 cars?
The tile pattern shown is made up of two different parallelograms in a tessellated pattern.
Find the area covered by the smaller tiles.
Find the area covered by the larger tiles.
Calculate the total area covered.
James used some scrap paper to make a birthday card in the shape of a parallelogram. The base of the card is 17\text{ cm} long, and the perpendicular height is 16\text{ cm}. Find the area of the card.
A roof in the shape of a parallelogram is to be entirely covered by identical solar panels that are also in the shape of a parallelogram. Each solar panel measures 1.2\text{ yd} along the longest side and has a perpendicular height of 0.6\text{ yd}.
Find the area covered by one solar panel.
Find the number of solar panels to be installed if the roof measures 23.04\text{ yd}^2 in area, and no part of the roof is to be left uncovered by solar panels.
An area measuring 2280\text{ cm}^2 is to be paved with identical tiles in the shape of parallelograms. Each tile measures 12\text{ cm} along the base, and has a perpendicular height of 5\text{ cm}.
Find the area that each tile covers.
How many tiles are needed to cover the whole area?
A quilt is made by sewing together 4 identical parallelograms as shown in the following figure:
If the total area of the quilt is 1944\text{ cm}^2, calculate the perpendicular height of each parallelogram piece.
