Question

An advertising banner has four sections, as modeled below. Two sections are congruent trapezoids, and two sections are congruent right triangles. Which measurement is the best estimate of the area of the banner in square meters.

Answer 1

Complete question is;

An advertising banner has four sections, as modeled in the attached image. Two sections are congruent trapezoids, and two sections are congruent right triangles. Which measurement is the best estimate of the area of the banner in square meters?

Answer:

6 m²

Step-by-step explanation:

Since we are told that there are two congruent trapezoid, it means that they will have same base of 1m.

This Means the total base of the entire triangle will be;

Base = 1 + 1¾ + 1 + 1¾ = 5.5 m

Height of main triangle = 2 m

Thus,

Area = ½ × 5.5 × 2 = 5.5 m²

We are looking for the best estimate, so let's approximate to the nearest whole number to get 6 m²

Answer 2

The best estimate is
`6m^2`

Explanation:

Given

See attachment for banner

Required

Estimate of the area

The banner has two congruent trapezoids and two congruent.

This means that, the two trapezoids have the same base lengths; the two triangles also have the same base lengths

So, we have:

`B_1 = 1 + 1 = 2` -- base lengths of both trapezoids

`B_2 = 1(3)/(4) + 1(3)/(4) = 1.75 + 1.75 = 3.5` -- base lengths of both triangles

The banner itself is a triangle and the dimension is:

`Height = 2m`

`Base = B_1 + B_2`

`Base = 2m + 3.5m = 5.5m`

So, the area is:

`Area = 0.5 * Base * Height`

`Area = 0.5 * 5.5m * 2m`

`Area = 5.5m^2`

The question asks for an estimate. So, we approximate.

`Area \approx 6m^2`