6.01 Area of triangles
Consider the rectangle shown:
Find the area of the entire rectangle.
Find the area of the triangle.
What do you notice about the two areas?
For each of the following figures:
Find the area of the entire rectangle.
Find the area of the shaded triangle.
Consider the following triangle:
Which dimension of the rectangle forms the height of the shaded triangle?
Find the area of the following triangles:
Find the area of a triangle which has the following dimensions:
For each of the following triangles, find the value of b or h given the area:
Area =20\text{ mm}^2
Area = 120 \text{ mm}^2
Area = 12 \text{ mm}^2
Area =48\text{ m}^2
Area = 54 \text{ cm}^2
Area = 120 \text{ cm}^2
Determine whether the following could be the dimensions of a triangle with an area of 20\text{ in}^2:
Base =8\text{ in}, height =5\text{ in}.
Base =1\text{ in}, height =20\text{ in}.
Base =5\text{ in}, height =8\text{ in}.
Base =2\text{ in}, height =20\text{ in}.
Complete the following table of base and height measurements for different triangles, which all have an area of 30\text{ m}^2:
| \text{Base (m)} | 10 | 15 | |
|---|---|---|---|
| \text{Height (m)} | 12 | ||
| \text{Area (m}^2) | 30 | 30 | 30 |
The faces on a 4-sided die are all triangular. Each face has a base length of 19\text{ mm} and a perpendicular height of 12\text{ mm}. Find the area of one face of the die.
Lisa has purchased a rectangular piece of fabric measuring 6\text{ yd} in length and 9\text{ yd} in width. Find the area of the largest triangular piece she can cut out from it.
A gutter running along the roof of a house has a cross section in the shape of a triangle as shown:
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.
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 meters above the sea bed.
At this point, they can cast a light out to view 9 meters 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 meters per second.
Find h, the distance of the divers from the sea bed at point P.
If the divers were descending directly downwards, how high above the sea bed were they 6 seconds before they reached point P?
At the entrance of the Louvre museum is a glass structure in the shape of a square base pyramid.
A replica of this pyramid is to be built such that each triangular face of the pyramid measures 7.5 meters at the base, and has a perpendicular height of 10 meters.
The faces will be made up of identical triangular glass tiles tessellated to fit exactly on each face.
Find the total area that needs to be covered with the triangular glass tiles.
How many glass tiles will be needed in total if each triangular tile measures 15 \text{ cm} across the base and has a perpendicular height of 20 \text{ cm}?