Find the missing side lengths of the following figures:
Find the unknown side length of a triangle if the perimeter is 64 \text{ mm} and two of the sides are 19 \text{ mm} and 21 \text{ mm}.
A rectangle has a perimeter of 22 \text{ cm}. If its length is 8 \text{ cm}, find its width.
A rectangle has a perimeter of 42 \text{ cm}. If its width is 7 \text{ cm}, find its length.
A square has a perimeter of 16 \text{ mm}. Find its side length.
What is the radius of the following circle?
Round your answer to two decimal places.
What is the radius of a circle with a circumference of length 30 \text{ m}? Round your answer to two decimal places.
Find the radius of the following sectors to two decimal places:
A sector has a contained angle of 50 \degree and an arc length of 13 \text{ cm}.
Find the size of the angle of the following sectors, in degrees. Round your answer to two decimal places.
A sector with radius 4.2 \text{ cm} and an arc length 14 \text{ cm}.
The perimeter of the following sector is 96.9 \text{ m}:
Use the formula P = 2 r + \dfrac{\theta}{180} \pi r, to find the size of the angle \theta, to the nearest degree.
Find the area of the sector. Round your answer to the nearest integer.
Find the width of the rectangle shown with an area of 24\text{ m}^2 and a length of 8\text{ m}:
Find the side length of a square with an area of 25\text{ mm}^2:
Find the length of a rectangle that has an area of 40\text{ cm}^2 and a width of 5 \text{ cm}.
Find the width of a rectangle that has an area of 27\text{ mm}^2 and a length of 9 \text{ mm}.
Find the length of each side of the square whose area is 64\text{ cm}^2.
Consider the following figure:
Find the value of x.
Find the value of y.
Hence, find the area of the shaded region in the figure.
Find the area of the shaded region in the figure shown:
Consider the following figure:
Find the value of x.
Find the value of y.
Hence, find the area of the shaded rectangle.
Find the perpendicular height, h, of the following triangle which has a base length of 6 \text{ cm} and an area of 54\text{ cm}^2.
Find the length of the base, b, in the following triangle if its area is 32\text{ m}^2.
Find the base of the triangle whose area is 17.5\text{ cm}^2 and height is 5 \text{ cm}.
The following table shows measurements for three different triangles that all have an area of 42\text{ cm}^2.
Find the value of:
| Triangle 1 | Triangle 2 | Triangle 3 | |
|---|---|---|---|
| \text{ Base (cm)} | A | 6 | 21 |
| \text{Height (cm)} | 28 | B | C |
| \text{Area (cm}^2) | 42 | 42 | 42 |
The following table shows measurements for three different parallelograms that all have an area of 70\text{ mm}^2:
| Parallelogram 1 | Parallelogram 2 | Parallelogram 3 | |
|---|---|---|---|
| \text{Base (mm)} | A | 10 | 35 |
| \text{Height (mm)} | 14 | B | C |
| \text{Area (mm}^2) | 70 | 70 | 70 |
Find the value of:
Find the base length of a parallelogram which has an area of 96\text{ cm}^2 and a perpendicular height of 8 \text{ cm}.
For each of the following parallelograms, find the value of the pronumeral using the given the area:
Area = 49\text{ mm}^2
Area = 32\text{ cm}^2
Area = 10\text{ m}^2
For each of the following trapeziums, find the value of the pronumeral using the given area:
Area = 24\text{ cm}^2
Area = 30\text{ cm}^2
Area = 36\text{ cm}^2
The area of a circle is 352\text{ cm}^{2}.
Find the length of its radius correct to two decimal places.
Find the circumference of the circle. Round your answer to one decimal place.
The area of the sector below is 2960.92\text{ m}^2.
Find the length of the radius. Round your answer to one decimal place.
Hence, find the perimeter of the sector. Round your answer to one decimal place.
Find the radius of the following sectors, given their angle and area. Round your answers to one decimal place.
Area of 30\text{ m}^2 and angle of 64 \degree
Area of 140\text{ m}^2 and angle of 230 \degree
Find the value of \theta, to the nearest degree, in the following sectors:
Area of 25.6\text{ mm}^2 and radius of 8 \text{ mm}
Area of 42 \pi \text{ m}^2 and radius of 14 \text{ m}
A sector has a radius of 10\text{ m} and an area of 65\text{ m}^2.
Find the included angle, \theta. Round your answer to the nearest degree.
Find the length of the resulting arc, l. Round your answer to the nearest metre.
Xavier is tiling his bathroom with equilateral triangle tiles. He knows the perimeter of each tile, but he wants to find the length of each side. If one tile has a perimeter of 51 \text{ cm}, how long is each side?
A satellite is orbiting the Earth at a height of h km above the Earth's surface. In one complete orbit, the satellite travels a distance of 41\,664 \text{ km}. If the radius of the Earth is 6400 \text{ km}, find the height of the satellite above the Earth.
Round your answer to one decimal place.
Rochelle keeps her goat in the same yard as her sprinkler. The sprinkler has a reach of 2.9 \text{ m}.
The sprinkler's default setting is to rotate back and forth over an angle of 60 \degree. Find the area of grass that it waters to two decimal places.
Rochelle wants to change the angle that the sprinkler rotates over so the goat has more watered grass to eat.
What angle will provide 9\text{ m}^2 of watered grass for the goat to eat? Round your answer to the nearest degree.
A quilt is made by sewing together 4 identical parallelograms as shown.
If the total area of the quilt is 1944\text{ cm}^2, determine the perpendicular height of each parallelogram piece.
A gutter running along the roof of a house has a cross-section in the shape of a triangle.
If the area of the cross-section is 40\text{ cm}^2, and the length of the base of the gutter is 10\text{ cm}, find the perpendicular height h of the gutter in metres.
