8.01 Areas of special quadrilaterals
The given parallelogram is formed into a rectangle:
Find the area of the rectangle.
Hence, find the area of the parallelogram.
The given parallelogram is formed into a rectangle:
Find an expression for the area of the rectangle in terms of b and h.
Hence, find an expression for the area of the parallelogram in terms of b and h.
Find the area of the following parallelograms:
Determine whether the following pairs of values could be the dimensions of a parallelogram with an area of 70 \,\text{mm}^2.
Base =10 \,\text{mm}, Height =7 \,\text{mm}
Base =7 \,\text{mm}, Height =10 \,\text{mm}
Base =1 \,\text{mm}, Height =70 \,\text{mm}
Base =2 \,\text{mm}, Height =70 \,\text{mm}
The given trapezium is split into a rectangle and a right-angled triangle:
Find the area of the rectangle.
Find the area of the triangle.
Hence, find the area of the trapezium.
The given trapezium is formed into a rectangle:
Find the length, l, of the rectangle.
Hence, find the area of the trapezium.
Two identical trapezia are put together to make a parallelogram:
Find the area of the entire parallelogram.
Find the area of one of the trapezia.
Two identical trapezia are put together to make a rectangle:
Find the area of the entire rectangle.
Find the area of one of the trapezia.
Two identical trapezia are put together to make a parallelogram:
Find an expression for the area of the entire parallelogram in terms of a, b and h.
Find an expression for the area of one trapezia in terms of a, b and h.
Find the area of the following trapeziums:
The given rhombus can be split into two triangles:
Find the area of one triangle.
Hence, find the area of the rhombus.
The given rhombus is formed into a rectangle:
Find the length of the rectangle in terms of y.
Find the width of the rectangle in terms of x.
Find the area of the rectangle in terms of x and y.
Hence, find the area of the rhombus in terms of x and y.
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{m}^2.
x = 2 \,\text{m} and y = 9 \,\text{m}.
x = 6 \,\text{m} and y = 3 \,\text{m}.
x = 12 \,\text{m} and y = 3 \,\text{m}.
x = 6 \,\text{m} and y = 6 \,\text{m}.
The given kite can be split into two triangles:
Find the area of one of the triangles.
Hence, 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.
Hence, find the area of the kite.
The given kite is formed into a rectangle:
Find the length of the rectangle in terms of y.
Find the width of the rectangle in terms of x.
Find the area of the rectangle in terms of x and y.
Hence, find the area of the kite in terms of x and y.
Find the area of the following kites:
Find the area of the following quadrilaterals:
For each of the following rhombuses, find the value of the pronumeral:
A = 64 \text{ cm}^{2}
A = 128 \text{ cm}^{2}
Rhombus ABCD has an area of \\ A = 55\,\text{cm}^2:
Given the diagonal BD = 11 \,\text{cm}, and \\ AC = x \,\text{cm}, find the value of x.
Rhombus ABCD has an area of 13 \text{ cm}^{2}:
If diagonal AC = 2, and diagonal BD = y, find the value of y.
The following kite has an area of 48 \,\text{cm}^2. The length of one of its diagonals is 12 \,\text{cm}:
Find the length of the other diagonal, k.
For each of the following kites, find the value of k:
A = 15 \text{ cm}^{2}
A = 22.5 \text{ cm}^{2}
A = 56 \text{ cm}^{2}
A = 137.5 \text{ cm}^{2}
For each of the following trapezia, find the value of the pronumeral:
A = 42 \,\text{mm}^2
A = 36 \text{ cm}^{2}
A = 20 \text{ m}^{2}
A = 24 \text{ cm}^{2}
Find the value of x if the area of the trapezium shown is 65 \text{ cm}^{2}:
Find the perpendicular height, h, of a parallelogram that has an area of 45 \,\text{cm}^2 and a base of 5 \,\text{cm}.
Find the base length, b, of a parallelogram that has an area of \, 216 \,\text{mm}^2 and a perpendicular height of 12 \,\text{mm}.
The area of a kite is 640 \text{ cm}^{2} and one of the diagonals is 59 \text{ cm}. If the length of the other diagonal is y \text{ cm}, find the value of y, rounded to two decimal places.
Complete the table of base and height measurements for three parallelograms that all have an area of 24 \,\text{m}^2:
| \text{Area}\, (\text{m}^2) | \text{Base} \, (\text{m}) | \text{Height}\, (\text{m}) |
|---|---|---|
| 24 | 8 | |
| 24 | 12 | |
| 24 | 6 |
Complete the table og the lengths of diagonal x and diagonal y for three kites that all have an area of 36 \,\text{mm}^2:
| \text{Area} \ (\text{mm}^2) | \text{Diagonal}, x \ (\text{mm}) | \text{Diagonal}, y \ (\text{mm}) |
|---|---|---|
| 36 | 18 | |
| 36 | 24 | |
| 36 | 12 |