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.
Find the perimeter of a square whose area is 49\text{ cm}^2.
Find the base of the triangle whose area is 17.5\text{ cm}^2 and height is 5 \text{ cm}.
Find the value of the pronumeral for each of the following triangles, given the area:
The area of this triangle is 54\text{ cm}^2:
The area of this triangle is 120 \text{ cm}^2.
The area of this triangle is 24 \text{ m}^2.
The area of this triangle is 120 \text{ mm}^2.
The area of this triangle is 32 \text{ cm}^2.
The area of this triangle is 12 \text{ mm}^2.
State whether the following pairs of values could be the dimensions of a triangle with an area of 27 \text{ mm}^2:
Base =9 \text{ mm}, height =6 \text{ mm}.
Base =6 \text{ mm} , height =9 \text{ mm}.
Base =1\text{ mm}, height =27\text{ mm}.
Base =2\text{ mm}, height =27\text{ mm}.
The following table shows measurements for three different triangles that all have an area of 42\text{ cm}^2:
| 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 |
Find the value of:
A family has 7.2 \text{ m}^2 of kitchen floor space for a rectangular bench.
If the width is fixed at 2 metres, and the bench is to take up all 7.2 \text{ m}^2, find the required length of the bench.
The kitchen bench will be made up of bench top pieces that measure 0.5 metres in width and 1.2 metres in length. Find the maximum number of bench top pieces that can be fitted along the width of the bench.
How many pieces of bench top pieces will be needed in total to create the bench top?
The kitchen floor is to be covered with tiles whose dimensions will be \dfrac{1}{8} the width of the bench, and \dfrac{1}{20} the length of the bench. How many tiles will be covered by the bench?
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 50 \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.
Deep sea divers are scanning an area of the sea bed where a boat capsized. They want to get to point P, which is h metres above the sea bed.
At this point, they can cast a light out to view 9 metres across the sea bed and a cross sectional area of 45 \text{ m}^2 of water. From side-on, the light casts a shape that looks like the diagram below. The divers descend at a rate of 1.2 metres per second.
Find h, the distance of the divers from the sea bed at the point P.
If the divers were descending directly downwards, how high above the sea bed were they 6 seconds before they reached point P?
