Unit 13

Areas and perimeters Area is the size of a figure on a two-dimensional surface. Perimeter is the distance around a given two-dimensional object.

So, area is the inside of a figure and perimeter is the measure of the line that sorrounds it. Here you have the most frequent areas and perimeters; use them in the activities that follow. In rectangles and squares:

Area We have to multiply its base by its height. In squares, all the sides measure the same.

Perimeter It’s the sum of its four sides.

In the rest of parallelograms:

Area

Perimeter

Multiply the measure of the longest side (called base) by its It’s the sum of its four sides. height (which is not the measure of the smaller side). In a rhombus:

Area

Perimeter

It can also be measured this way: Multiply the length of its It’s the sum of its four sides. two diagonals (D and d) and then divide the product by two. In a trapezium:

Area

Perimeter

First, sum the measure of its two parallel sides (called bases: It’s the sum of its four sides. B and b); then, multiply the result by its height (distance between both bases); finally, divide the product by two. In a triangle:

Area

Perimeter

First, multiply the base (one of its sides) by its height or It’s the sum of its three sides. altitude; then, divide it by two. In right triangles, the height is equal to one of the sides (or catheti). In the rest of polygons:

Area

Perimeter

First, divide the polygon in triangles; then calculate their It’s the sum of all its sides. In areas (as if they were isolated); finally sum their products. regular ones, multiply sides. In a circle:

Area

Perimeter

If r is its radius and π is 3.14, then we’ll obtain 2 the area with this operation: π · r 2 For a circle sector: calculate π · r ; then divide it by 360 and finally multiply that product by the degrees of the arc.

Multiply its diameter by 3.14 (called π); or also: 2π · r For an arc: calculate 2π r; then divide it by 360 and finally multiply that product by the degrees of the arc.

Activities about areas and perimeters: 1. Give names to these figures; measure them and calculate their areas and perimeters: 1.

2.

3.

4.

5.

6.

2. Give names to these figures; measure them and calculate their areas and perimeters: a.

b.

c.

3. Calculate the areas and perimeters of the following figures (use Pythagoras's theorem): Right triangle: catheti 8 and 6 cm.

Circle: radius 9 cm.

Regular hexagon:: radius 6 cm; side 6 cm.

Rhombus:: its diagonals are 6 and 10 cm.