Question

Construct the trapeziums with the given measures and also find their area.
AIMS with AI || SM, AI = 6 cm, IM = 5 cm, AM = 9 cm and MS = 6.5 cm
$\left[5\right]$

Answer 1

Given
AI = 6cm
IM = 5cm
AM = 9cm, and AI || SM
MS = 6.5 cm

Construction
Steps:
Draw a line segment AI = 6cm.
With A and I as centres, draw arcs of radii 9 cm and 5 cm respectively and let them cut at M
Join AM and IM.
Draw MX parallel to AI With M as centre, draw an arc of radius 6.5 cm cutting MX at S.
Join AS AIMS is the required trapezium.
$\left[1\right]$
$\left[3\right]$
Calculation of Area:
Area of the trapezium AIMS = 12 x h x (a + b) sq.units
= 12 x 4.6 x (6 + 6.5)
= 12 x 4.6 x 12.5
Area of the trapezium AIMS = 28.75 Sq.cm
$\left[1\right]$